A narrow beam of light is incident on a glass plate of refractive index 1.6. It makes an angle `53^@` with normal to the interface. Find the lateral shift of the beam at the point of emergence, if thickness of the plate is 30 mm. (Take sin`53^@` = 0.8.)

Options

A. 9.023 mm
B. 15.52 mm
C. 13.53 cm
D. 13.53 mm

Answer

A, C, D

Explanation

For incident ray,
`n_1sintheta_1=n_2sin theta_2`
(1) `sin53^@=1.6sintheta_2`
0.7986=1.6`sintheta_2`
`thereforesin theta_2=(0.7986)/(1.6)=0.4991 ~~0.5 " rad "=30^@`
Now, lateral shift,
`x=(tsin(theta_1-theta_2))/(costheta_2)`
`=(30sin(53^@-30^@))/(cos30^@)=(30sin23^@)/(cos30^@)`
`=(30xx0.3907)/(0.866)=13.53` mm