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Question

A ray of light from a liquid (μ=3) is incident on a system of two right angled prism of refractive indices 3and2 as shown in the figure. The light suffers zero net deviation when it emerges into air from surface CD. If the angle of incidence (in degrees) is 5n. Find n ?
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Solution
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First, we apply the law of refraction for the interface AC,
The incident angle will be 90i

3sin(90i)=2sinr

3cosi=2sinr

Now, for the interface CD,

2sin(90r)=sini

Thus, 2cosr=sini

We have two equations in i and r, squaring and adding these 2,
we get,
2cos2i+1=2

This gives, cos i=12

Thus, i=45

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