Question

draw a neat labelled ray diagram of refraction of a plane wavefront at a plane surface.​

Answer 1

Explanation:

Reflection of plane wave at plane surface:-

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

Reflection of plane wave at plane 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/v1 + OQ/v1

where v1 is the velocity of the wave. From figure (3)

Reflection of plane wave at plane surface

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

ii) Refraction of plane waves at plane surfaces:-

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

v1 be the speed of light in medium 1 and v2 the speed of light in medium 2

Refraction of plane waves at plane surfaces

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

Reflection of plane wave at plane surface

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

Reflection of plane wave at plane surface

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