1. Division of Amplitude

2. Optical beam splitter

3. Fringes of equal inclination

4. Thin Film InterferenceA B C D C D B t i A d

5. Optical path difference for the first two reflected beams

6. Path Difference

8. 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

9. Phase shift

10. Condition for maxima
Condition for minima

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

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

13. Fringes of equal inclination

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

15. Fringes of equal thickness
Constant height contour of a topographial map

16. Fizeau Fringes
Beam splitter
Extended source n n2 n x

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

18. Consecutive fringes are separated by

19. Wedge between two plates1 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

21. 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

25. Reflected Newton’s Ring

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