Question

Prove mathematically that lateral displacement depend upon the thichkness slab

Answer 1

"If the glass slab were not present, the incident ray would travel a distance a in the horizontal direction. When the glass slab is present, the ray only travels a distance b due to refraction. The lateral displacement s is therefore

s=a−b

We find a and b using some simple geometry from the figure.

a=dtanθ1

b=dtanθ2

However, we can calculate θ2 from θ1 using Snell’s law.

n1sinθ1=n2sinθ2

θ2=sin−1(n1n2)

Plugging this expression for θ2 into the equation for b gives

b=dtan[sin−1(n1n2)]=dn1/n21−(n1/n2)2√

The lateral displacement s is

s=dtanθ1−dn1/n21−(n1/n2)2√=d[tanθ1−n1/n21−(n1/n2)2√]

"