Question

# A Newton’s Rings interferometer uses a plano-convex lens1 having refractive index ?. = 1.523 and a...

1. A Newton’s Rings interferometer uses a plano-convex lens1 having refractive index ?. = 1.523 and a sodium source with ? = 589 nm. The laterally moving microscope finds the radius of the 6th dark fringe to be equal to 7 mm. (a) Determine the focal length of the plano-convex lens. (b) A drop of coconut oil (?567 = 1.46) fills the space between the curved surface of the lens and the flat surface of the mirror determine the radii of the third and 10th dark fringes.

is wavelength of light used and R is radius of curvature of planoconvex lens.

7 mm = ( 6*589*10-6mm*R)1/2
R = 1.386x104 mm = 13.86 m

Focal length of planoconvex lens
f = R/(n-1)     n is refractive index of lens material
f = 13.86 m/ (1.523 -1)
=26.51 m

With liquid between curved surface of lens and flat surface of mirror, radius of n th dark fringe

where is refractive index of liquid
r3 = ( 3*589x10-6mm*1.386x104mm / 1.46)1/2
= 4.09 mm
r10 = ( 10*589x10-6mm*1.386x104mm / 1.46)1/2
= 7.48 mm