A ray of light is incident on a surface of glass slab at an angle `45^@`. If the lateral shift produced per unit thickness is `1//sqrt3`, the angle of refraction produced is

Options

A. `tan^(-1) ((sqrt(3))/(2))`
B. `tan^(-1) (1 - sqrt((2)/(3)))`
C. `sin^(-1) (1 - sqrt((2)/(3)))`
D. `tan^(-1) ( sqrt((2)/(sqrt(3) - 1)))`

Answer

B

Explanation

Lateral shift
`d = (t sin (i-r))/( cos r ) `
`rArr " " (d)/(t) = (sin (i-r))/(cos r ) = (sin i cos r - cos i sin r )/( cos r )`
`rArr " " (1)/(sqrt(3)) = sin 45^(@) - cos 45^(@) tan` r
`rArr " " (1)/(sqrt(3)) = (1)/(sqrt(2)) (1 - tan r) rArr r = tan^(-1) (1 - sqrt((2)/(3)) ) `.