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Question

A ray of light is travelling from air into a medium in which its velocity is reduced to 34 of its velocity in air. If it is incident at a very small angle on the surface of separation, and if i and r are the angles of incidence and reflection respectively, then the deviation of the ray is given by?

A
δ=isin1(43sini)
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B
δ=i2
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C
δ=i4
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D
δ=2r
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Solution

The correct option is A δ=isin1(43sini)
We know that deviation of the ray δ = angleofincidence(i)angleofrefraction(r) -------(1)
Also from Snell's law we get
sinisinr=μ=vmva,where vmandva are the velocity of light in medium and air respectively.
Given when light travels from air to medium its velocity decreases by a factor of 34 times the speed of light in air.
Thus reducing the above values in Snell's law we get,
sinisinr=3va4vasinr=43sinir=sin1(43sini)
Thus equation 1 becomes
δ=isin1(43sini)

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