Question

A circular beam of light (diameter d) falls on a plane surface of a liquid. The an gl e of i n ci d en ce i s 4 5 0 and the refractive index is  . The diameter of refracted beam is

Answer 1

Explanation:

See the figure and then see this explanation

Taking triangle 1

cos i = d /PQ

Taking riangle 2

cos r = d' / Pq

cosi/d = cos r /d'

d' = d cos r /cosi ------ 1

Using snell's law ,

μ = sin i / sinr = sin 45 /sinr

sinr = 1/(√2μ )

sin²Ф + cos²Ф = 1

cos r = √( 2μ² -1) / √2μ

d' = d √( 2μ² -1) / μ