- Introduction
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- Wave fronts and rays
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- Huygens’s principle
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- Reflection of and Refraction of plane waves using Huygens’s principle
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- Principle of Superposition of waves
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- Interference of light waves
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- Coherent Sources
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- Conditions for sustained interference of light waves
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- Young Double slit experiment
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- Theory of interference fringes
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- Displacement of fringes

- Consider the figure given below which shows incident and reflected wave fronts when a plane wave fronts travels towards a plane reflecting surface

- POQ is the ray normal to both incident and reflected wave fronts

- The angle of incidence i and angle of reflection r are the angles made by incidence and reflected rat respectively with the normal and these are also the angles between the wave fronts and the surface as shown in the figure 3

- The time taken by the ray POQ to travel from incident wave front to then reflected one is

Total time from P to Q= t=PO/v_{1}+ OQ/v_{1}

where v_{1}is the velocity of the wave. From figure (3)

- There can be different rays normal to incident wave front and they can strike plane reflecting surface at different point O and hence they have different values of OA

- Since tome travel by each ray from incident wave front to reflected wave front must be same so, right side of equation (1) must be independent of OA.This conditions happens only if

(sini-sin r)=0

or i=r

Thus law of reflection states that angle of incidence i and angle of reflection are always equal

- Consider the figure given below which shows a plane surface AB separating medium 1 from medium 2

- v
_{1}be the speed of light in medium 1 and v_{2}the speed of light in medium 2

- Incident and refracted wave front makes angles i and r
^{'}with surface AB where r^{'}is called angle of refraction

- Time taken by ray POQ to travel between incident and refracted wave fronts would be

- Now distance OA would be different for different rays .So time t should be independent of any ray we might consider

- This can be achieved only if coefficient of OA in equation (2) becomes equal to zero or

- Equation (3) is nothing but
where n is called the reflective index of second medium with respect to the first medium.*Snell’s law of refraction*

- The ratio of phase velocity of light c in vacuum to its value v
_{1}in a medium is called the refractive index n_{1}( or μ_{1}) of the medium .Thus

- When light travels from medium 1 to medium 2,what we measure is the refractive index of medium 2 relative to medium 1 denoted by n
_{12}( or μ_{12}).Thus

where n_{1}is refractive index of medium 1 with respect to vacuum and n_{2}is refractive index of medium 2 w.r.t. vacuum

- When light travels from one medium to another the frequency ν=1/T remains same i.e.
*ν*_{1}=*ν*_{2}

- Since the velocities of light v
_{1}and v_{2}are different is different medium ,the wavelength λ_{1}and λ_{2}are also different i.e.,

the wavelength of light in the medium is directly proportional to phase velocity and hence inversely proportional to the refractive index

- When two or more sets of waves travel through a medium and cross one another the effects produced by one are totally independent of the

- At any instant the resultant displacement of a particle in the medium depends on the phase difference between the waves and is the algebraic sum of the displacement it would have at the same instant due to each separate set. This is known as the principle of superposition of waves and forms the basis of whole theory of interference of waves discovered by Young in 1801

- If at any instant
**y**,_{1}**y**,_{2}**y**,--- are the displacements due to different waves present in the medium then according to superposition principle resultant displacement_{3}**y**at any instant would be equal to the vector sum of the displacements (**y**,_{1}**y**,_{2}**y**) due to the individual waves i.e.,_{3}

- The resultant displacement of the particles of the medium depends on the amplitude ,phase difference and frequency of the superposing waves

- Consider two waves of same frequency f and wavelength λ travelling through a medium in the same direction and superpose at any instant of time say t

- Equation of these waves at time t is

where φ is the phase difference between the waves

- According to principle of superposition of waves ,resultant displacement of particles equals

Now from trigonometry identity

Putting it in equation (8) we find

Let us suppose

Putting them in equation (9) we have

where

- We know that intensity of waves is proportional to its amplitude i.e.

Class 12 Maths Class 12 Physics

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