Find the displacement of the ray after it imerges from `CD`
.

Options

A. `2.5 cm`
B. 5 cm
C. 1 cm
D. `(sqrt(13))/(3) cm`

Answer

A

Explanation

by shell's law `2 sin 30^(@) = sqrt(13) sin r`
`1 = sqrt(13) sin r`
`sin gamma =(1)/(sqrt(13)), tan r=(1)/(sqrt(12))`
So, lateral displacement `= (t sin (i-r))/(cos r)`
`= (t[sin(i)cos r-cos(i)sinr])/(cos r)`
`=t[sin i-cos i tan r]`
`10[sin30-cos 30 xx (1)/(sqrt(12))]`
`= 10[(1)/(2)-(sqrt(3))/(2)xx(1)/(2 sqrt(3))]=2.5 cm`.