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Question

A ray of light undergoes refraction and loses 0.25 times its velocity. If 'i' is the angle of incidence and is very small, the angle of deviation for the ray of light is______


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Solution

Step 1: Given data

  1. The angle of incidence =i
  2. v2=v1-0.25v1=0.75v1

Step 2: Formula used

  1. μ1sini=μ2sinr
  2. μ2μ1=ν1v2
  3. δ=i-r

Step 3: Solution

Let δ be the angle of deviation

By Snell's law

μ1sini=μ2sinr......(1)

Also,

μ2μ1=ν1v2......(2)Refractiveindex=speedofthelightinvaccumspeedoflightinthegivenmedium

From (2)

μ2μ1=10.75

Putting the above value in (1)

sinr=0.75·sini

r=0.75i ifθissmall,sinθθ

So, the angle of deviation is, δ=i-r

δ=i-0.75iδ=0.25i

Hence, the angle of deviation is 0.25i.


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