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Question

A cubical block of glass of refractive index n1=32 is in contact with the surface of water of refractive index n2=43. A beam of light is incident on the vertical face of the block. After refraction, a total internal reflection occurs at the base and refraction at the opposite face takes place. The ray emerges at angle θ as shown. The value of θ is given by


A
sinθ>176
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B
cosθ>176
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C
sinθ<176
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D
cosθ<176
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Solution

The correct option is C sinθ<176

For total internal reflection at AB,

i>θc

sini>sinθc
[All angles less than 90]

cosi<cosθc ............(1)

For refraction at BC, from Snell's law,

n1sinr=n3sinθ

32sin(90i)=1×sinθ

cosi=23sinθ

23sinθ<cosθc [from (1)]

23sinθ<1sin2θc

sinθ<32    1⎜ ⎜ ⎜4332⎟ ⎟ ⎟2 [sinθc=n2n1]

sinθ<176
Why this question?

Caution - Be careful in inequalities of sinθ and cosθ. For angle less than 90, sinθ is an increasing function and cosθ is a decreasing function.

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