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A uniform,horizontal beam of light is in...

A uniform,horizontal beam of light is incident upon a quarter cylinder of radius`R=5`cm and has a refractive index `2//sqrt(3)`.A patch on the table for a distance `'x'`from the cylinder is unilluminated ,find the value of `'x'`?

Text Solution

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The correct Answer is:
`5cm`

`(2)/(sqrt(3))sinC=1 sin 90^@`
`sinC=(sqrt(3))/(2)……..(1)`
`cos C=(R )/(R+x)`
`sqrt(1-sin^(2)C)=(R )/(R+x)……(2)`
from(1)and (2)
`sqrt(1-(3)/(4))=(R )/(R+x)`
`(1)/(2)=(R )/(R+x)`
`2R=R+x`
` R=x`
`x=5`
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