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Q.

A slab made of a transparent material, has refractive index μ . A ray of light is incident on the top face of the slab at on angle of incidence of  30o. Then the minimum value of μ for which no ray of light will emerge from the lateral surface AB of the block is

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a

32

b

52

c

12

d

23

answer is B.

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Detailed Solution

α=(90o-r)The ray QR will not emerge from the face ABif α>θc⇒sinα>sinθc⇒sin(90o-r)>1μ⇒cosr>1μ⇒1-sin2r>1μ⇒1-sin2θμ2>1μ⇒μ>1+sin2θ⇒μmin=1+sin230o=52
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A slab made of a transparent material, has refractive index μ . A ray of light is incident on the top face of the slab at on angle of incidence of  30o. Then the minimum value of μ for which no ray of light will emerge from the lateral surface AB of the block is