Prasanna

Students can Download Chapter 3 Use of Spread Sheet in Business Application Notes, Plus Two Accountancy Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Accountancy Notes Chapter 3 Use of Spread Sheet in Business Application

Business Applications
The following accounting applications are done with the help of spreadsheet

• Payroll Accounting
• Asset Management
• Loan Repayment

Pay Roll Accounting
Payroll is a statement prepared to show the detailed salary calculation of employees. It contains Basic
Pay, Dearness Allowance, Travelling Allowance, Provident Fund Contribution, ESI Premium, etc. The computation of salary payment is based on the number of days an employee has worked, rate per grade, rate of allowances and deductions to be made therefrom.

1. Preparation of Salary Bill:
The preparation of salary bill should provide for the following:

• Maintaining payroll related data such as Employee No., Name, attendance, Basic Pay, DA, and other allowances, deductions to be made, etc.
• Periodic Payroll Computations: It includes the calculation of various earnings and deductions.
• Preparation of salary statement and employee’s salary slip.
• Generation of advice to bank: It contains the net salary to be transferred to individual bank account of employees and other salary related statutory payments such as provident fund, tax, etc.

2. Pav Roll Components:
The following elements are important for salary computation and its payment.

Earnings:

• Basic Pay (BP): It is the pay in the pay scale
• Grade Pay (GP): It is the pay to be added to the basic pay according to the designation.
• Dearness Pay (DP): Portion of dearness allowance merged with Basic Pay
• Dearness allowance (DA): Compensation for erosion in the purchasing power of wage earner due to Price rise.
• House Rent Allowance (HRA): An amount paid as rent of residential accommodation.
• Transport Allowance (TA): It is an amount to faclitate commuting to the palace of work.

Deductions:

• Professional TAX: Statutory deduction levied by State Government.
• Provident Fund (PF): It is a statutory deduction under provident Fund Act. It is deducted from salary as a part of social security.
• Tax Deducted at Source (TDs)- Monthly deduction towards income Tax liability of an employee.
• Recovery of Loan instalment: An amount deducted on account of any loan taken up by employee.

3. Net Salary Calculation:
Step 1: Calculate Gross salary by using the given formula.

Step 2: Calculate Total Deduction by using the following formula.
Total Deduction = Professional Tax + Provident Fund + Tax deducted at source + Loan Recovery + Any other deductions.

Step 3: Calculate net salary by the given formula
Net Salary = Gross salary – Total Deduction.

Asset Accounting
Assets are resources of the organisation. Assets which are used in the business for more than one year, called Fixed assets. The value of Fixed assets may be reduced due to depreciation. The gradual and permanent diminution in the value of assets due to wear and tear is called depreciation.

The depreciation on fixed assets is provided to recognise the cost of the asset consumed during an accounting period since the life of such assets extends beyond single accounting year.
Total amount of Depreciation – Acquisition cost – Salvage value.

1. Methods of calculation of depreciation:

• Straight Line Method (SLM)
• Written Down Value Method (WDV)

Straight Line Method
Under this method a fixed amount is deducted from the value of an asset year after year on account of depreciation and debited to profit and loss account. This method is also called Fixed Instalment method, or Original Cost method. Under this method value of asset will be reduced to zero.
Depreciation = \(\frac{\text { cost of the asset }-\text { Scrap Value }}{\text { Life of the asset }}\)

1. Cost of the asset/Acquisition cost = Purchase Price + Other expenses directly related with the asset (ie., carriage inward, freight, installation, renewal or reparis, Pre operating expenses).

2. Scap value / salvage value: It is the value of an asset which is realisable at the end of its useful life. Salvage value is the estimated residual value of depreciable asset or property at the end of its economical or useful life.

3. The depreciation under straight line method is computed by using the built in LibreOffice calc function SLN.

Written Down Value Method (WDV)
This method is also known as Diminishing balance method or Reducing balance method. Under this method, a fixed percentage is written off every year on the book value of the asset at the beginning of the year. Here the amount of depreciation goes on decreasing and there fore, the book value of asset will not become zero after its working life.
Amount of depreciation = Written Down Value of asset × Rate of depreciation

1. This method is also called Declining Balance (DB) method and uses the LibreOffice Calc function DB to compute the depreciation.

Loan Repayment Schedule
Loan is a sum of borrowed money for a specified period at a pre-specified rate of interest. The loan is repaid through a number of periodic repayment instalments over the loan repayment period.

LibreOffice Calc function PMT is used to calculate loan repayment schedule. The parameters of the function PMT are as follows.

Students can Download Chapter 1 Electric Charges and Fields Notes, Plus Two Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Physics Notes Chapter 1 Electric Charges and Fields

Introduction
You may have seen a spark (or a crackle sound), when we take off our synthetic clothes. Have you ever tried to find any explanation for this phenomenon? Do you know the reason for lightning?

The above phenomenon can be explained on the basis of static electricity. Static means anything that does not change with time. Electrostatics deals with the properties of charges at rest.

Electric Charge
It is found experimentally that the charges are of two types:

1. Positive charge
2. Negative change

The unit of charge is Coulomb (c).
Note: Positively charged body means deficiency of electrons in the body and a negatively charged body means excess of electrons.

Gold-Leaf electroscope: A simple apparatus to detect charge on a body is called a gold-leaf electroscope.

Apparatus: It consists of a vertical metal rod placed in a box. Two thin gold leaves are attached to its bottom end as shown in figure.

Working: A charged object touches the metal knob at the top of the rod. Charge flows on to the leaves and they diverge. The degree of divergence is an indicator of the amount of charge.

Conductors And Insulators
Conductors: Conductors are those substances which allow passage of electricity through them.
Insulators: Insulators are those substances which do not allow passage of electricity through them.

1. Earthing (Or) Grounding:
When a charged body bring in contact with earth, all the excess charge pass to the earth through the connecting conductor. This process of sharing the charges with the earth is called grounding or earthing. Earthing provides protection to electrical circuits and appliances.

Charging By Induction
A body can be charged in different ways.

1. Charging by friction
2. Charging by conduction
3. Charging by induction

1. Charging by friction:
When two bodies are rubbed each other, electronsin one body (in which electrons are held less tightly) transferred to second body (in which electrons are held more tightly).

Explanation: When a glass rod is rubbed with silk, some of the electrons from the glass are transferred to silk. Hence glass rod gets +ve charge and silk gets -ve charge.

2. Charging by conduction:
Charging a body with actual contact of another body is called charging by conduction.
Explanation:

If a neutral conducting body (A) is brought in contact with positively charged conducting body (B), the neutral body gets positively charged.

3. Charging by induction:
The phenomenon by which a neutral body gets charged by the presence of neighboring charged body is called electrostatic induction.
Explanation:
Step I: Place two metal spheres on an insulating stand and bring in contact as shown in figure (a).

Step II: Bring a positively charged rod near to these spheres. The free electrons in the spheres are attracted towards the rod. Hence, one side of the sphere becomes negative and the other side becomes positive as shown in the figure (b).

Step III: Separate the spheres by a small distance by keeping the rod nearto sphere A. The two spheres are found to be oppositely charged as shown in figure (c).

Step IV: Remove the rod, the charge on spheres rearrange themselves as shown in figure (d).

In this process, equal and opposite charges are developed on each sphere.

Basic Properties Of Electric Charge
1. Unlike charges attract and like charges repel.

2. Charge is conserved : Changes can neither be created nor be destroyed.
Explanation: When a glass rod is rubbed with silk, some of the electrons from the glass are transferred to silk. Hence glass rod gets +ve change and silk gets -ve changes.

3. Electric Charge is Quantized: Change on any body is the integral multiple of electronic charge. This is called quantization of charge.
i.e. q = ± ne, n = 1, 2, 3, ……….

4. Additivity of Charges: If a system contains n charges q₁, q₂, q₃,……..q_n, then the total change of the system is q₁ + q₂ + q₃ +……+q_n.

Coulomb’S Law
Statement: The force between two stationary electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Explanation:

Consider two point charges q₁ and q₁. which are separated by a distance ’r’. The force between the changes.
\(\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{q}_{1} \mathrm{q}_{2}}{\mathrm{r}^{2}}\)
vector form: The force F₁₂ (on the first charge by second} is given by (vector form)

Forces Between Multiple Charges
Super position principle: If the system contains a number of interacting changes, then the force on a given charge is equal to the vector sum of the forces exerted on it by all remaining charges.
Explanation:

Consider a system of three charges q₁ q₂ and q₃ as shown in figure.
The force on q₁ due to q₂
\(\overrightarrow{F_{12}}=\frac{1}{4 \pi \varepsilon_{0} r_{12}^{2}} r_{12}^{\wedge}\)
Similarly the force q₁ due to q₃
\(\overrightarrow{F_{13}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r_{13}^{2}} r_{13}^{\wedge}\)
The total force F₁ on q₁ (due to q₂ and q₃) can be written as

System of ‘n’ charges: If system contains ‘n’ charges, total force acting on q₁ due to all other charges.

Electric Field
The concept electric field is introduced to explain the interaction between two charges.
Electric field intensity: Strength or intensity of the electric field at any point is defined as the force acting on a unit positive charge placed at that point.
Mathematical expression of electric field intensity:

Consider a charge q (test charge) at a distance ‘r’ from a source charge Q.
The force acting on q due to Q.
\(\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{Qq}}{\mathrm{r}^{2}}\)
If q = 1, the force acting on this unit charge due to Q
\(\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{Q}}{\mathrm{r}^{2}}\)
This force is called electric field intensity at a distance ‘r’ due to the charge Q.
ie; \(E=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r^{2}}\)

1. Electric field due to a system of charges:
Consider a system of charges q₁, q₂………..q_n. Let P be point at distances r_1p, r_2p,………..r_np from charges. q₁, q₂,……..q_n respectively. According to super position principle, total electric field at ‘p’ due to all other charges,

2. Physical Significance Of Electric Field:
Question 1.
What are the importance of the concept of electric field?
Answer:

• Electric field explains the electrical environment of a system of charges.
• Electric field help us to explain the interaction between two charges at rest or in motion.

Electric Field Lines
Properties of Electric Lines of Force

(Field lines due to some simple charge configurations)

1. An electric line of force originates from positive charge and ends on negative charge.
2. The tangent drawn at a point on an electric line of force will give the direction of electric field at that point.
3. Two lines of force never intersect each other. (If they cut each other, at the point of intersection there will be two tangents. This indicates that there will be two directions of electric field at the same point which is impossible).
4. The number of electric lines of force passing normally through an area is directly proportional to the strength of the electric field.
5. The relative density of the field lines indicates the relative strength of electric field.
6. Electric field lines due to static charge never form closed loops.
7. In a uniform electric field, lines of force are parallel.

Electric Flux

Consider a closed surface. Let ∆\(\vec{S}\) be a small area element on the surface. The electric field lines (E) passes through this area element at an angle θ. Electric flux ∆Φ through an area element ∆\(\vec{S}\) is defined by

The direction of area vector d\(\vec{S}\) is perpendicular to the surface.

Electric Dipole
Electric dipole: A pair of equal and opposite charges separated by small distance is called electric dipole. Dipole moment (p): Electric dipole moment (p) is defined as product of magnitude of charge and dipole length.
Dipole moment p = q × 2a
q – charge, 2a – dipole length
Dipole moment is a vector, directed from negative to positive charge.

1. Electric field at a point on the axial line of an electric dipole: Consider an electric dipole of moment P = 2aq. Let ‘S’ be a point at a distance ‘r’ from the centre of the dipole.

Electric field at ‘S’ due to point charge at ‘A’

Directed as shown in figure. Electric field at ‘S’ due to point charge at ‘B’

Directed as shown in figure. Therefore resultant electric field at ‘S’
And its magnitude E = E_B + -E_A

P = q × 2a
We can neglect a2 because a<<r.
∴ Electric field at S,

This can be written in vector form as

The direction is along E_B.
The field due to an electric dipole is directed from negative charge to positive charge along the axial line.

2. Electric field due to a dipole at a point on the perpendicular bisector of the dipole (at a point on the equatorial line).

Consider a dipole of dipole moment P = 2aq. Let ‘S’ be a point on its equatorial line at a distance ‘r’ from its centre. The magnitudes of electric field at ‘S’ due to +q and -q are equal and acts as shown in figure. To find the resultant electric field resolve

Their normal components cancel each otherwhere as their horizontal components add up to give the resultant field at ‘S’.
E = E_Acos θ + E_Bcos θ = 2 E_B cos θ

The direction of the field due to the dipole at a point on the equatorial line is opposite to the direction of dipole moment.

3. Physical significance of dipole: The molecules of dielectrics may be classified into two classes:
(i) Polar molecules: In polar molecule, the centres of negative charges and positive charges do not coincide. Therefore they have a permanent
Example: H₂0, HCl, etc.

(ii) Nonpolar molecule: In nonpolar molecule, the centres of negative charges and positive charges coincide. Therefore they have no permanent electric dipole moment.
Example: C0₂, CH_4, etc.
Note: In the presence of external electric field, a nonpolar molecule becomes a polar molecule.

Dipole In A Uniform External Field

Consider an electric dipole of dipole moment P = 2aq kept in a uniform external electric field, inclined at an angle θ to the field direction.

Equal and opposite forces +qE and -qE act on the two charges. Hence the net force on the dipole is zero. But these two equal and opposite forces whose lines of action are different. Hence there will be a torque.
torque = any one force × perpendicular distance (between the line of action of two forces)
τ = qE × 2 a sin θ
Since P = 2aq
τ = P E sin θ
Vectorialy \(\vec{\tau}=\vec{P} \times \vec{E}\)
This torque tries to align the dipole along the direction of the external field.
Special Case:

• When θ = 0 ; τ =0
• When θ = 90; τ = PE, the maximum.

Note: In uniform electric field dipole has only rotational motion

Dipole in nonuniform electric field:
Question 2.
What happens to dipole if the applied electric field is nonuniform?
Answer:
In nonuniform electric field, the net force and torque acting on the dipole will not be zero. Hence the dipole undergoes for both translational and rotational motion.

Continuous Charge Distribution
Charges on a body may be distributed in different ways according to the nature of body. Depending upon this distribution of charge, we deal with different types of charge densities,

1. Line charge density, λ
2. Surface charge density, σ or
3. Volume charge density, ρ

1. Linear charge density (λ): Charge per unit length is called linear charge density. If ∆Q is the charge contained in a line element ∆l,
Linear charge density λ = \(\frac{\Delta Q}{\Delta l}\)

2. Surface charge density (σ): Charge per unit area is called surface charge density. If ∆Q is the charge contained in a area element ∆s, surface charge density can be written as
σ = \(\frac{\Delta Q}{\Delta S}\)

3. Volume charge density (ρ): Charge per unit volume is called volume change density. If ∆Q is the charge contained in a volume ∆v, volume charge density.
ρ = \(\frac{\Delta Q}{\Delta v}\)

Gauss’s Law
Gauss’s theorem states that the total electric flux over a closed surface is 1/ε₀ times the total charge enclosed by the surface.
Gauss’s theorem may be expressed

Proof:

Consider a charge +q .which is kept inside a sphere of radius ‘r’.

Important points regarding Gauss’s law:

• Gauss’s law is true for any closed surface.
• Total charge enclosed by the surface must be added (algebraically). The charge may be located anywhere inside the surface.
• The surface that we choose for the application of Gauss’s law is called the Gaussian surface.
• Gauss’s law is used to find electric field due to system of charges having some symmetry.
  Gauss’s law is based on the inverse square of distance. Any violation of Gauss’s law will indicate departure from the inverse square law.

Applications Of Gauss’s Law
Gauss’s law can be used to find electric field due to system of some symmetric charge configurations. Some examples are given below.

1. Field Due To An Infinitely Long Straight Uniformly Charged Wire:

Consider a thin infinitely long straight rod conductor having change density λ. (λ = \(\frac{q}{l}\))
To find the electric field at P, we imagine a Gaussian surface passing through P.
Then according to Gauss’s law we can write,

Integrating over the Gaussian surface, we get (we need not integrate the upper and lower surface because, electric lines do not pass through these surfaces.)

2. Field Due To A Uniformly Charged Infinite Plane Sheet

Consider an infinite thin plane sheet of change of density σ. To find electric field at a point P (at a distance ‘r’ from sheet), imagine a Gaussian surface in the form of cylinder having area of cross section ‘ds’.
According to Gauss’s law we can write,

(Since q = σds)
But electric field passes only through end surfaces ,so we get ∫ds = 2ds

E is directed away from the charged sheet, if a is positive and directed towards the sheet if a is negative.

3. Field Due To A Uniformly Charged Thin Spherical Shell: Consider a uniformly changed hollow spherical conductor of radius R. Let ‘q’ be the total charge on the surface.

To find the electric field at P (at a distance r from the centre), we imagine a Gaussian spherical surface having radius ‘r’.
Then, according to Gauss’s theorem we can write,

The electric field is constant, at a distance ‘r’. So we can write,

Case I: Electric field inside the shell is zero.
Case II: At the surface of shell r = R

Students can Download Chapter 10 Wave Optic Notes, Plus Two Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Physics Notes Chapter 10 Wave Optic

Introduction
In 1678, the Dutch physicist Christian Huygens put forward the wave theory of light. We will discuss in this chapter.

Wavefront:
The wavefront is defined as the locus of all points which have the same phase of vibration. The rays of light are normal to the wavefront. Wavefront can be divided into 3.

1. Spherical wavefront
2. Cylindrical wavefront
3. Plane wavefront.

1. Spherical Wavefront:

The wavefront originating from a point source is spherical wavefront.

2. Cylindrical Wavefront:

If the source is linear, the wavefront is cylindrical.

3. Plane wavefront:
If the source is at infinity, we get plane wavefront.

Huygen’s Principle
According to Huygen’s principle

1. Every point in a wavefront acts as a source of secondary wavelets.
2. The secondary wavelets travel with the same velocity as the original value.
3. The envelope of all these secondary wavelets gives a new wavefront.

Refraction And Reflection Of Plane Waves Using Hygens Principle
1. Refraction of a plane wave. (To prove Snell’s law):
AB is the incident wavefront and c₁ is the velocity of the wavefront in the first medium. CD is the refracted wavefront and c₂ is the velocity of the wavefront in the second medium. AC is a plane separating the two media.

The time taken for the ray to travel from P to R is

O is an arbitrary point. Hence AO is a variable. But the time to travel a wavefront from AB to CD is constant. In order to satisfy this condition, the term containing AO in eq.(2) should be zero.

where ¹n₂ is the refractive index of the second medium w.r.t. the first. This is the law of refraction.

2. Reflection of plane wave by a plane surface:

AB is the incident wavefront and CD is the reflected wavefront, ‘i’ is the angle of incidence and ‘r’ is the angle of reflection. Let c₁ be the velocity of light in the medium. Let PO be the incident ray and OQ be the reflected ray.
The time taken for the ray to travel from P to Q is

O is an arbitrary point. Hence AO is a variable. But the time to travel for a wave front from AB to CD is a constant. So eq.(2) should be independent of AO. i.e., the term containing AO in eq.(2) should be zero. AO
∴ \(\frac{A O}{C_{1}}\)(sin i – sin r) = 0
sin i – sin r= 0
sin i = sin r
i = r
This is the law of reflection.
Behavior of wave frond as they undergo refraction or reflection.

a. Wave frond through the prism:

Consider a plane wave passing through a thin prism. The speed of light waves is less in glass. Hence the lower portion of the incoming wave frond will get delayed. So outgoing wavefrond will be tilted as shown in the figure.

b. Wave frond through a thin convex lens:

Consider a plane wave passing through a thin convex lens. The central part of the incident plane wave travels through the thickest portion of lens.

Hence central part get delayed. As a result the emerging wavefrond has a depression at the centre. Therefore the wave front becomes spherical and converges to a point F.

c. Plane wave incident on a concave mirror:

A plane wave is incident on a concave mirror and on reflection we have spherical wave converging to the focul point F.

3. The Doppler Effect:
There is an apparent change in the frequency of light when the source or observer moves with respect to one another. This phenomenon is known as Doppler effect in light.

When the source moves away from the observer the wavelength as measured by the source will be larger. The increase in wavelength due to Doppler effect is called as red shift.

When waves are received from a source moving towards the observer, there is an apparent decrease in wavelength, this is referred to as blue shift.

Mathematical expression for Doppler shift:
The Doppler shift can be expressed as

V_radial is the component of source velocity along the line joining the observer to the source.

Coherent And Incoherent Addition Of Waves
Super position principle:
According to superposition principle, the resultant displacement produced by a number of waves at a particular point in the medium is the vector sum of the displacements produced by each of the waves.

Coherent sources:
Two sources are said to be coherent, if the phase difference between the displacements produced by each of the waves does not change with time.

Incoherent sources:
Two sources are said to be coherent, if the phase difference between the displacements produced by each of the waves changes with time.

Constructive interference:
Consider two light waves meet together at a point. If we get maximum displacement at the point of meeting, we call it as constructive interference.

Destructive interference:
Consider two lightwaves meet together at a point. If we get minimum displacement at the point of meeting, we call it as destructive interference.

Mathematical condition for Constructive interference and Destructive interference:

Consider two sources S₁ and S₂. Let P be point in the region of s₁ and s₂. The displacement produced by the source s₁ at P.
y₁ = a cos ωt
Similarly, the displacement produced by the source s₂ at P
y₂ = a cos (ωt + Φ)
Where Φ is the phase difference between the displacements produced by s₁ and s₂
The resultant displacement at P,
Y = y₁ + y₂
= a cos ωt + a cos (ωt + Φ)
= a (cos ωt + cos (ωt + Φ))

Therefore total intensity at P,

Constructive interference:
If we take phase difference Φ = 0, ±2π, ±4π……., we get maximum intensity (4I₀) at P. This is the mathematical condition for constructive interference. The condition for constructive interference can be written in the form of path difference between two waves.

Where n = 0, 1, 2, 3……..

Destructive interference:
If we take phase difference Φ = ±π, ±3π, ±5π………., we get zero intensity at P. This is the mathematical condition for destructive interference. The condition for destructive interference can be written in the form of path difference between two waves.

Where n = 0, 1, 2, 3……..

Interference Of Light Waves And Youngs Double Slit Experiment
Young’s double-slit experiment:

The experiment consists of a slit ‘S’. A monochromatic light illuminates this slit. S₁ and S₂ are two slits in front of the slit ‘S’. A screen is placed at a suitable distance from S₁ and S₂. Light from S₁ and S₂ falls on the screen. On the screen interference bands can be seen.

Explanation:
If crests (ortroughs) from S₁ and S₂ meet at certain points on the screen, the interference of these points will be constructive and we get bright bands on the screen.

At certain points on the screen, crest and trough meet together. Destructive interference takes place at those points. So we get dark bands.

Expression for band width:

S₁ and S₂ are two coherent sources having wave length λ. Let ‘d’ be the distance between two coherent sources. A screen is placed at a distance D from sources. ‘O’ is a point on the screen equidistant from S₁ and S₂.
Hence the path difference, S₁O – S₂O = 0
So at ‘O’ maximum brightness is obtained.
Let ‘P’ be the position of n^th bright band at a distance x_n from O. Draw S₁A and S₂B as shown in figure. From the right angle ∆S₁AP
we get, S₁P² = S₁A² + AP²
S₁P² = D² + (X_n – d/2)² = D² + X_n² – X_nd + \(\frac{d^{4}}{4}\)
Similarly from ∆S₂BP we get,
S₂P² = S₂B² + BP²
S₂P² = D² + (X_n + d/2)²

S₂P² – S₁P² = 2x_nd
(S₂P + S₁P)(S₂P – S₁P) = 2x_nd
But S₁P ≈ S₂P ≈ D
∴ 2D(S₂P – S₁P) = 2x_nd
i.e., path difference S₂P – S₁P = \(\frac{x_{n} d}{D}\) ____(1)
But we know constructive interference takes place at P, So we can take
(S₂P – S₁P) = nλ
Hence eq(1) can be written as

Let x_n+1 be the distance of (n+1)^th bright band from centre o, then we can write

This is the width of the bright band. It is the same for the dark band also.

Diffraction
The bending of light round the comers of the obstacles is called diffraction of light.

1. The single slit diffraction:

Consider a single slit AC having length ‘a’. A screen is placed at suitable distance from slit. B is midpoint of slit, A straight line through B (perpendicular to the plane of slit), meets the screen at O. AD is perpendicular CP.

Calculation of path difference:
Consider a point P on the screen having a angle θ with normal AE. The path difference between the rays (coming from the bottom and top of the slit) reaching at P,
CP – AP = CD
(CP – AP) = a sin θ
path difference, (CP – AP) = a θ______(1)
[for small θ. sin θ ≈ θ]

(I) Position of maximum intensity:
Consider the point ‘O’, the path difference between the rays (coming from AB and BC) reaching at O is zero. Hence constructive interference takes place at ‘O’. Thus maximum intensity is obtained. This point is called central maximum or the principal maximum.

(II) Position of secondary minima:
Let P be a point on the screen such that the path difference between the rays AP and CP be λ.
ie, CP – AP = λ______(2)
Substituting eq (1) in eq (2) we get
θ = λ
(or) θ = \(\frac{\lambda}{a}\)______(3)
Let the slit AC be imagined to be split into two equal halves AB and BC. For every point in AB, there is a corresponding point in BC such hat the distance between the points are equal to a/2 Consider two points K and L such that, KL = a/2. There fore, the path difference between the rays (coming form K and L) at P is,.
LP – KP = \(\frac{a}{2}\)θ_______(4)
Substituting (3) in (4) we get

This means that the rays (coming from K and L) reaching at P are out of phase and cancel each other. Hence the intensity at P becomes zero.
In otherwards, at angle θ = \(\frac{\lambda}{\mathrm{a}}\)
The intensity becomes zero.
Similarly on the lower half of the screen, the intensity is zero for which θ = – \(\frac{\lambda}{\mathrm{a}}\)
The general equation for zero intensity can be written as
θ = \(\pm \frac{n \lambda}{a}\)
Where n = 1, 2, 3,…
For first minima n = 1, and second minima n = 2.

(III) Position of Secondary maxima:
Let P be a point on the screen, such that
CP – AP = \(\frac{3}{2}\)λ
From eq (1),we know (CP – AP) = aθ
Therefore aθ = \(\frac{3}{2}\)λ
The wave front AC can be divided into three equal parts.

The rays from first and second parts will cancel each other and the rays from third part will reach at P. Hence the point P becomes bright.

Similarly the next maximum occurs at θ = \(\frac{5}{2}\)\(\frac{λ}{a}\)
The general equation for maximum can be written
\(\theta=\pm \frac{(2 n+1) \lambda}{2 a}\)

1. (a) Intensity Distribution on the screen of diffraction pattern:

(b) Comparison between interference and diffraction bands:
Interference:

• Interference is due to superposition of waves coming from two wavefronts.
• Interference bands are of equal width.
• Minimum intensity regions are perfectly dark.
• All the bright bands are of equal intensity.

Diffraction:

• Diffraction is due to the superposition of waves coming from different parts of the same wave front.
• Diffraction bands are of unequal width.
• Minimum intensity regions are not perfectly dark.
• All bright bands are not of the same intensity.

2. Seeing The Single Slit Diffraction Pattern:

Take two razor blades and an electric bulb. Hold the two blades as shown in the figure. Observe the glowing bulb through the slit. A diffraction pattern can be seen.

3. Resolving Power Of Optical Instruments:
Resolving power of optical instrument:
The ability of an optical instrument to form distinctly separate images of the two closely placed objects is called is resolving power.

Explanation:

The image of a point object formed by a ideal lens is a point only. But because of diffraction effect, instead of point image, we get a diffraction pattern. Diffraction pattern consists of a bright central circular region surrounded by concentric dark and light rings.

Let us discuss three cases; when we observe two point object through a lens.

1. Unresolved:
If central maxima of two diffraction pattern are overlapped, the image is unresolved. This image can’t be viewed clearly.

2. Just resolved:
If central maxima of two diffraction pattern are just separated, the image is just resolved. In this case image is just distinqushed.

3. Resolved:
If central maxima of two diffraction pattern are separated, the image is resolved. This image can be viewed clearly.

Limit of resolving power of optical instrument:
The minimum distance of separation between two points so that they are just resolved by the optical instrument is known as its limit of resolution. Resolving power is also defined as reciprocal of limit of resolution.

1. Telescope and resolving power:

Telescope consist of two convex lenses called eyepiece and objective .The light falling on objective lens undergoes for diffraction. Hence a diffraction pattern of bright and dark rings is produced around central bright region as shown in figure.
The radius of central bright region,

This radius can be written in terms of angular width,
∆θ ≈ \(\frac{0.61 \lambda}{\mathrm{a}}\)
Where a is the radius and f – focal length of objective lens. λ is the wave length of light used.

This angular width of central bright region is related to resolving power of telescope. When angular width of spot increases, resolving power decreases.

The limit of resolution of telescope, ∆θ ≈ \(\frac{0.61 \lambda}{\mathrm{a}}\)
This equation shows that telescope will have better resolving power if ‘a’ is large and λ is small.

2. Microscope and resolving power:

In microscope the object (microscopic size) is placed slightly beyond f (focal length of objective lens). When the separation between two points in a microscopic specimen is comparable to the wavelength λ of light, the diffraction effect become important.

Where nsinβ is called numerical aperture, n is the refractive index of liquid used in microscope, β is the half angle of the cone of light from the microscopic object with objective lens.
The limit of resolution of microscope d_min = \(\frac{1.22 f \lambda}{2 n \sin \beta}\)
This equation also can be written as d_min = \(\frac{1.22 \lambda}{2 \tan \beta}\)

Note: Telescope is used to resolve objects at far distance but microscope is used to produce magnification of near objects.

4. The Validity Of Ray Optics:
Fresnel distance is the distance beyond which the diffraction properties becomes significant, (ie. the ray optics is converted into wave optics).
Fresnel distance, z_F = \(\frac{\mathrm{a}^{2}}{\lambda}\)
Where ‘a’ is the size of the aperture
For distances much smaller than z_F, the spreading due to diffraction is smaller compared to the size of the beam. It becomes comparable when the distance is approximately z_F. For distances much greater than z_F, the spreading due to diffraction dominates over that due to ray optics.

Polarisation

Consider a long string that is held horizontally, the other end of which is assumed to be fixed. If we move the end of the string up and down in a periodic manner, a wave will propagate in the +xdirection (see above figure). Such a wave can be described by the following equation
y(x,t) = a sin (kx – ωt)
where ‘a’ represent the amplitude and k = 2π/λ represents the wavelength associated with the wave.

Since the displacement (which is along the y-direction) is at right angles to the direction of propagation of the wave, this wave is known as a transverse wave.

Also, since the displacement is in the/direction, it is often called to as a y-polarised wave. Since each point on the string moves on a straight line, the wave is also called to as a linearly polarised wave.

The string always remains confined to the x-y plane and therefore it is also called to as a plane polarised wave.

In a similar manner we can consider the vibration of the string in the x-z plane generating a z-polarised wave whose displacement will be given by
z(x,t) = a sin (kx – ωt)

Unpolorised wave:
If the plane of vibration of the string is changed randomly in very short intervals of time, then it is known as an unpolarized wave.

(a) Polarization property of light:
When light passes through certain crystals like tourmaline, the vibrations of electric field vector are restricted. This property exhibited by light is known as polarization.

Note:

1. Polarization is the property of light which reveals that light is a transverse wave.
2. A sound wave can’t be polarized because sound wave is a longitudinal wave.

Polarizer and analyzer:
When an unpolarized light passes through a tourmaline crystal T₁, the light coming out of T₁ is plane polarized.

In order to check the polarization, another tourmaline crystal T₂ is kept parallel to T₁.

When we look through T₂ we get maximum intensity. Then T₂ is rotated through 90°. If no light is coming, we can say that light from T₁ is plane polarized.

Polarizer: The crystal which produces polarized light is known as polarizer.

Analyzer: The crystal which is used to check weather the light is polarized or not is called the analyzer or detector.

Law of Malus: This law states that when a beam of plane polarized light is incident on an analyzer, the intensity (I) of the emergent light is directly proportional to the square of the cosine of the angle (θ) between the polarizing directions of the polarizer and the analyzer.

I = I_m cos²θ
where I_m is the maximum intensity.

1. Polarisation By Scattering:

The nunpolarized light incident on a dust particle in atmosphere, it is absorbed by electrons in the dust particle. The electrons in the dust particle reradiate light in all directions. This phenomenon is called scattering.

Explanation:
Let a beam of unpolarized light be incident on a dust particle along x-axis. The electrons in the dust particle absorb light and behave as a oscillating dipole. This dipole emit light in all directions.

When an observer observe this particle along y-axis, the observer can receive light from the electron vibrating in z-axis. This light is linearly polarised in z-direction (its plane of polarisation is yz).

This polarised light is represented by dots in the picture. This explains the polarisation of scattered light from the sky.

2. Polarization By Reflection:
At a particular angle of incidence on a medium, the reflected lights is fully polarized. This angle is known as polarizing angle or Brewster’s angle. At polarizing angle, the reflected and refracted rays are mutually perpendicular.

Brewster’s law:
Brewster’s law states that the tangent of the polarizing angle is equal to the refractive index of the material of the reflector.

Let ‘Q ’ be the polarizing angle and ‘n’ be the refractive index of the medium then,
tan θ = n
At polarizing angle, r + θ =90°.

Proof:
Consider an unpolarized light coming from air and is incident on a medium having refractive index n. Let θ be the angle of incidence, Φ be the angle of reflection and ‘r’ be the angle of refraction.
Using snells law, we can write
n = \(=\frac{\sin \theta}{\sin r}\) ______(1)
At the polarizing angle reflected and refracted light are mutually perpendicular
ie. Φ – 90 + r = 180°
∴ r = 90 – Φ______(2)
Substituting eq (2) in eq(1), we get

But we know
Angle of incidence (θ) = angle of reflection(Φ)
∴ n = \(\frac{\sin \theta}{\cos \theta}\)
n = tanθ

Students can Download Chapter 1 Overview of Computerised Accounting System Notes, Plus Two Accountancy Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Accountancy Notes Chapter 1 Overview of Computerised Accounting System

Introduction
Computerised Accounting System refers to the process of accounting transaction through the use of hardware and software in order to produce accounting records and reports, i.e. Journals, Ledgers, Trial Balance, Profit and Loss Account and Balance Sheet.

Data and Information
Data is raw, unorganised facts that need to be processed. Data can be something simple and useless until it is organised. When data is processed, organised, structured or presented in a given context so as to make it useful, it is called information. A computer is an information processing machine. Computers process data to produce information.
Example:

Components of Computerised Accounting System (CAS)

1. Procedure: A logical sequence of actions to perform a task.
2. Data: The raw fact for any business operation.
3. People: Users of computerised accounting system
4. Hardware: The physical components of a computer.
5. Software: A set of programmes to do a work.

Salient Features of Computerised Accounting System (CAS)
1. Simple and Integrated:
Computerised accounting system is designed to integrate all the business operations such as sales, finance, purchase, etc.

2. Accuracy and speed:
Computrised Accounting system provides data entry forms for fast and accurate data entry of the transactions.

3. Scalability:
The system can cope easily with the increase in the volume of business transactions. The software can be used for any size and type of the organisation.

4. Security:
This system is highly secured and the data and information can be kept confidential.

5. Reliability:
Computerised accounting system makes sure that the critical financial information is accurate, controlled and safe from data corruption.

Grouping of Accounts
Grouping of accounts means classifying the ledger accounts and organising them under major heads of accounts. These main groups ascertain whether a ledger affects profits and Loss Account as a revenue item or it affects the Balance Sheet. It helps in presenting summarised reports and information. Basically, there are Five account groups viz. Capital, Assets, Liabilities, Income, and Expenditure.

1. Reserved or Default Groups:
All accounting packages have predefined account groups. They are called reserved groups. They are:

• Account groups of Trading Account
• Account groups of Profit and Loss Account
• Account groups of Balance Sheet

2. Account groups of Trading Account:

• Sales Account
• Purchases Account
• Direct Expenses Account
• Direct Incomes Account

3. Account groups of Profit and Loss Account:

• Indirect Incomes
• Indirect Expenses

4. Account groups of Balance Sheet:
A. Liability Side

1. Capital account
2. Reserves and Surplus
3. Loans
4. Long Term Liabilities
5. Current Liabilities
   • Sundry creditors
   • Bank overdraft
   • Outstanding expenses
   • Provisions

B. Assets side

1. Fixed Assets
2. Investments
3. Current Assets
   • Cash in hand
   • Cash at bank
   • Sundry Detors
   • Stock in hand
4. Miscellaneous Expenses

Codification of Accounts
Giving a numerical number or alphabet or both to a particular account for identification is known as codification of accounts.
1. Types of Codes:
a. Sequential codes:
Here numbers or alphabets are.assigned in consecutive order. These codes are applied primarily to source documents such as cheques, invoices, etc.
(i) Name of customers:

(ii) Name of suppliers:

b. Block Codes:
In Block codes, a range of numbers is alloted to a particular account group. Here, numbers within a range follow sequential coding scheme.
Room Numbering System of a Lodge:

Coding of Dresses:

c. Mnemonic codes:
A mnemonic code consists of alphabets or abbreviations as symbols to codify an account.

Methodology to Develop Coding Structure
Let us examine the 15 digit Goods and Services Tax Identification Number (GSTIN). GSTIN is a 15 digit unique code which is assigned to each tax payer, which will be statewise and PAN-based.
GSTIN Format or Structure:

From the above details, we can identify that GSTIN is a combination of state code, PAN, number of registration within the state, default digit and check code to detect errors.
Another Example:
Let us examine how to develp a coding strucutre for students in Thrissur district under DHSE. The first step is to develop hierarchy of the school system and attributes of the students.

Entry year	4 digit
School code	5 digit
Course code	2 digit
Roll Number	2 digit

Thus we allocate 13 digit code to a student.

Security Features of Computerised Accounting Software
Every accounting software ensures data security, safety and confidentiality by providing the features like Password Security, Data Audit and Data Vault.
1. Password Security:
Password is the key to allow the access to the system. Computerised accounting system protects the unauthorised persons from accessing to the business data. Only authorised person, who is supplied with the password, can enter to the system.

2. Data Audit:
It enables one to know as to who and what changes have been made in the original data there by helping and fixing the responsibility of the person who has manipulated the data and ensures data integrity.

3. Data Vault:
Software provides additional security through data encryption. Encryption means scrambling the data so as to make its interpretation impossible.

Advantages of Computerised Accounting System (CAS)

1. Financial reports can be prepared in time.
2. Alterations and additions in transactions are easy and gives the changed result in all books of accounts instantly.
3. It ensures effective control over the system.
4. Economy in the processing of accounting data.
5. Confidentiality of data is maintained.
6. The closing balance of one financial year is automatically carried forward to next financial year.

Limitations of Computerised Accounting System

1. Faster Obsolescence of technology necessitates frequently upgradation in accounting software.
2. Data may be lost or corrupted due to power interruption.
3. Un programmed reports can not be generated.
4. Alterations in transactions are easy. This reduces the reliability of accounting work.
5. Work with CAS is expensive.

Accounting Information System (AIS)
Accounting Information System (AIS) and its various subsystems may be implemented through Compterised Accounting System (CAS). Such system of AIS are described below.

1. Cash and Bank subsystem: Receipts and payments of cash.
2. Sales and Accounts Receivable sub system: Maintaining of sales and Receivables ledgers.
3. Inventory subsystem: Purchase and sale of goods. Specifying the price, quantity, and date.
4. Purchase and Accounts Payable sub system: Maintaing of purchase and payable leadgers.
5. Pav Roll Accounting sub system: Payment of salaries and wages.
6. Fixed Assets Accounting sub system: Purcahses, additions, sale and usage of fixed assets.
7. Expense Accounting sub system: Various types of expenses.
8. Tax Accounting sub system: Deals with GSTIN, Income Tax etc.
9. Final Accounts sub system: Preparation of final accounts.
10. Costing sub system: Ascertainment of cost of goods produced.
11. Budget sub system: Preparation of budgets.
12. Management information sub system (MIS): Preparation of reports that are vital for management decision making.