A uniform horizontal beam of light is incident upon a prism as shown. The prism is in the shape of a quarter cylinder of radius R = 5 cm and has index of refraction μ = 1.5. A patch on the table top for a distance x from the cylinder is unilluminated. The value of x in cm is.
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Ans. 1
Sol.
x = (y + z) – R
y = h tan θ c
z = h cot θ c
x = h[tan θ c + cot θ c] – R
sin θ c = 
= 
= 
⇒ h = 
x = 
– R
= 1.71 cm
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