A ray `R_(1)` is incident on the plane surface of the glass slab (kept in air) of refractive index `sqrt(2)` at angle of incident equal to the critical angle for this air glass system. The refracted ray `R_(2)` undergoes partial reflection & refraction at the other surface. The angle between the reflected ray `R_(3)` and the refracted ray `R_(4)` at that surface is :

Options

A. `45^(@)`
B. `135^(@)`
C. `105^(@)`
D. `75^(@)`

Answer

C

Explanation

From Snell's law `sqrt(2)"sin"I = 1 "sin"90^(@)`

`I'= 45^(@)`
`therefore "Again 1 . "sin"45^(@) = sqrt(2)"sin"r`
`r= 30^(@)` & `sqrt(2)"sin"30^(@) = 1 "sin"r'`
`r'= 45^(@)`
Hence `theta = 180^(@) - (30+45^(@)) = 105^(@)`