Question

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.

Answer 1

Radius of nth dark fringe

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