Question

The spherical surface of a plano-convex lens of radius of curvature R=1m is gently placed on
a flat plate. The space between them is filled with a transparent liquid of refractive index 1.55. The

refractive indices of the lens and the flat plate are 1.5 and 1.6 respectively. The radius of the sixteenth
dark Newton’s ring in the reflected light of wavelength λ is found to be √5 mm.

(i) Determine the wavelength λ (in microns) of the light.

(ii) Now, the transparent liquid is completely removed from the space between the lens and the flat plate. Find the radius (in mm) of the twentieth dark ring in the reflected light after

this change.​

Answer 1

Answer:

Explanation:

The condition for minima are

r2Rn2=(k+12)λ,

(There occur phase changes at both surfaces on reflection, hence minima when path difference is half interger multiple of λ).

In this case k=4 for the fifth dark ring

(Counting from k=0 for the first dark ring).

Thus, we can write

r=(2K−1)λR/2n2−−−−−−−−−−−−−−√,K=5

Substituting we get r=1.17mm.