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/(sqrt(3))`m, 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

Here angle of incidence `i=45^(@)`
`("lateral shift" (d))/("thickness of as glass slab"(t))=1/(sqrt(3))`
Angle of refraction `r=?`
`d=(t sin delta)/(cos r)=(t sin (i-r))/(cos r)impliesd/t=(sin (i-r))/(cos r)`
Using `sin(A-B)=sinA cos B-cosA sin B`
`:.d/t=(sin i cos r -cos i sin r)/(cos r)`
or `d/t=sin i-cos i tan r`
Substituting the values of the given quantities we get
`1/(sqrt(3))=sin 45^(@)-cos 45^(@)tan r`
or `1/(sqrt(3))=1/(sqrt(2))(1-tan r)`
or `(sqrt(2))/(sqrt(3))=1-tan r` or `tan r=1-sqrt(2/3)`
or `r=tan^(-1)(1-sqrt(2/3))`