In the figure (a) the light is incident at an angle `theta` (slightly greater than the critical angle). Now keeping the incident ray fixed a parallel slab of refractive index `n_3` is placed on surface AB.(fig b)

Options

A. total internal reflection occurs at AB for `n_(3)ltn_(1)`
B. total internal reflection occurs at AB for `n_(3)gtn_(1)`
C. the ray will return back to the same medium for all values of `n_(3)`
D. total reflection occurs at `CD` for `n_(3)ltn_(1)`

Answer

A, C

Explanation

In first case
`sic C=(n_(1))/(n_(2))`
in second case if
`n_(3)n_(1)`
(A). `sinC^(')=(n_(3))/(n_(2))ltsinC`
`C^(')ltC`
TIR will donee at surface AB
(B). If `n_(3)gtn_(1)`
`sinC^(')gtsinC`
`C^(')gtC`
ray will not undergo TIR at AB
(C).
if `n_(3)gtn_(1)`
`n_(2)sinC=n_(2)sinr`
`sinr=(n_(2))/(n_(3))sinC`
`=(n_(2))/(n_(3))sinC`
`=(n_(2))/(n_(3))xx(n_(1))/(n_(2))`
`sinr=(n_(1))/(n_(3))=sinC^('')`
ray will be undergo TIR at CD.