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(sqrt3/2)`
B. `tan^-1(1-sqrt(2/3))`
C. `sin^-1(1-sqrt(2/3))`
D. `tan^-1(sqrt((2)/(3-1)))`

Answer

B

Explanation

Lateral shift `y=(tsin(i-r))/(cosr)`
`y/t=(sin(i-r))/(cosr)=(sinicosr-cosisinr)/(cosr)`
`=sini-cositanr`
`1/sqrt3=sin45^@-cos45^@tanr=1/sqrt2(1-tanr)`
`sqrt(2/3)=1-tanr`
`tanr=1-sqrt(2/3)`
`r=tan^-1(1-sqrt(2/3))`