Question

In Newton's ring experiment the diameter of bright ring is reduced to 0.8 of its value after introducing a liquid below the convex surface.calculate the refractive index at liquid.

Answer 1

We can write for radius of bright ring

$r_{k}=\frac{\sqrt{(2k-1)Rλ}}{\sqrt{2n}} (1)$

In our two cases

$r_{1}=\frac{\sqrt{(2k-1)Rλ}}{\sqrt{2}} (2)$

$r_{2}=\frac{\sqrt{(2k-1)Rλ}}{\sqrt{2n}} (3)$

According to the condition of the problem, we have

$r_{2}=0.8 r_{1} (4)$

We put (2) and (3) in (4)

n=1.5625

Answer

1.5625