Figure shows a ray of light entering and passing through a dense glass slab and emerging from the side. If the angle `i=60^(@),` slab thickness b= 0.04 m and the refractive index of glass `=sqrt(3)`, the parallel shift d between the emerging and entering rays in mm is

Options

A. `sqrt((3)/(4)`
B. `sqrt((4)/(3)`
C. `(40)/sqrt(3)`
D. `15sqrt(3)`

Answer

C

Explanation

We have, `sinr= (sini)/(mu)= (sin60^(@))/sqrt(3)=(1)/(2)`
`rArr` Angle of refraction, `r= 30^(@)`
Now , lateral shift d is given by
d = t.sec ( r ) .sin (i - r)
`=0.04xxsec(30^(@)).sin (60^(@)-30^(@))=0.04xxtan 30^(@)`
`=(0.04)/sqrt(3)m = (0.04xx1000)/(sqrt(3))mm = (40)/(sqrt(3))mm`