Division of Amplitude

Optical beam splitter

Fringes of equal inclination

Thin Film Interference A B C D C D B t i A d

Optical path difference for the first two reflected beams

Path Difference

Phase Changes Due To Reflection An electromagnetic wave undergoes a phase change of 180° upon reflection from a medium of higher index of refraction than the one in which it was traveling Analogous to a reflected pulse on a string μ2 μ1

Phase shift

Condition for maxima Condition for minima

For n1 > nf > n2 n1 < nf < n2 Condition for maximum Condition for minima

say n1=n2=n n > n f n < n f

Fringes of equal inclination

Haidinger’s Bands: Fringes of equal inclination Beam splitter P x f Extended source Focal plane Dielectric slab PI P2

Fringes of equal thickness Constant height contour of a topographial map

Fizeau Fringes Beam splitter Extended source n n2 n x

Fizeau Fringes: fringes of equal thickness Conditions for maximum These are termed Fizeau fringes.

Consecutive fringes are separated by

Wedge between two plates 1 2 glass D t glass air x Path difference = 2t Phase difference  = 2kt -  (phase change for 2, but not for 1) Maxima 2t = (m + ½) o/n Minima 2t = mo/n

Newton’s Ring Ray 1 undergoes a phase change of 180 on reflection, whereas ray 2 undergoes no phase change R= radius of curvature of lens x=radius of Newton’s ring

Reflected Newton’s Ring

Reference 1. Optics Author: Eugene Hecht Class no. 535 HEC/O Central library IIT KGP