Question

A system of coordinatees is drawn in a medium whose refractive index vaires as `mu=(2)/(1+Y^(2))` where `0 le y le 1`. A ray of light is incident at origin at an angle `60^(@)` with y-axis as shown in figure. At point P, the ray becomes parallel to x-axis, the volue of H is -

A. `{((2)/(sqrt3))-1}^(1//2)`
B. `{(2)/(sqrt(3))}^(1//2)`
C. `{(sqrt(3)) - 1}^(1//2)`
D. `((4)/(sqrt(3)) -1}^(1//2)`

Answer 1

Correct Answer - A
`mu"sin"theta_(1) = mu_(2)"sin"theta_(2) implies ` at origin x =0 , y=0 `implies mu = 2 "&" theta= 60^(@)`
at point `P : theta = 90^(@) implies 2"sin"60^(@) = mu"sin"90^(@) implies sqrt(3) = (2)/(y^(2)+1) implies y= [((2)/(sqrt(3))) -1]^(1//2)`