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/(sqrt3-1)))`

Answer

B

Explanation

(b) Here, angle of incidencei=`45^(@)`
`("Lateral shift(d)")/("Thickness of glass slab(t)")=1/sqrt3`
Lateral shift,d=`(tsindelta)/(cosr)=(tsin(i-r))/(cosr)`
`rArr d/t=(sin(i-r))/(cosr)`
or `d/t=(sinicosr-cosisinr)/(cosr)`
`=(cosr-sinr)/(sqrt2cosr)`
or `d/t=1/sqrt2(1-tanr)or1/sqrt3=1/sqrt2(1-tanr)`
or `tanr=1-(sqrt2)/(sqrt3)`
or Angle of refraction, r=`tan^(-1)(1-(sqrt2)/(sqrt3))`