Answer to Question #92612 in Optics for ROHIT SHARMA

Question

A Plano-convex lens of radius 1.0 m is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the 15th and 5th dark rings in the reflected light are
5.90X10−3 m × and 3.36 X10−3 m. Next, the space between the lens and the glass plate is filled with a liquid. The diameter of the 5th ring changes to 3.0X10−3 m. Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is 589 nm

Answer 1

(i) We can write for dark ring

$r_{k}=\frac{\sqrt{kRλ}}{\sqrt{n}} (1)$

In our case, k=5, R=1 m, r5=1.5×10-3 m, λ=589 nm

Using (1) we get: n=1.308

Answer

1.308

(ii) We can write for bright ring

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

In our case, k=5, R=1 m, r5=1.5×10-3 m, λ=589 nm

Using (2) we get: n=1.178

Answer

1.178