IIT JEE , AIEEE Forum - Physics , Optics

apples

a uniform,horizontal beam of light is incident upon a quarter cylinder of radius R = 5cm,and has a refractive index of 2/

3.

a patch on the table for a distance 'x' from the cylinder is unilluminated

find the value of

x

elessar_iitkgp

Consider a ray falling normally on the edge of the quarter cylinder.
sin90 / sinr = 2/

3
r = 60
This ray strikes the other side of the quarter cylinder and refracts back into air.
Point where it strikes the other side = R/

3 from the centre
For the second refraction,
sin 30 / sin r' =

3/2
sin r' = 1/

3
tan r' = 1/2
[R(

3-1)/

3]/x = 1/2
x = 2R(

3-1)/

3 = 10(

3-1)/

3