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Question

A glass prism of refractive index 1.5 is immersed in water (μ=4/3). Light beam incident normally on the face AB is totally reflected to reach the face BC if
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A
sinθ>8/9
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B
2/3<sinθ<8/9
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C
sinθ2/3
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D
cosθ8/9
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Solution

The correct option is A sinθ>8/9
Given -- μg=1.5,μw=4/3

As the light beam is normal to prism surface AB, so it will enter in prism without any deviation. Same will happen with water surface. Now the beam will reach to face BC, when it gets total internal reflection from surface AC.
θ=θ, because angle between two lines is equal to the angle between perpendiculars of the two lines.

We have the condition for total internal reflection,

sinθ>1/wμg

or sinθ>μw/μg

or sinθ>(4/3)/1.5

or sinθ>8/9

594726_294978_ans.PNG

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