1. 15-1: Interference
Interference, a phenomenon that occurs when two light beams meet.
If the two beams enhance each other to give a brighter beam, it is called constructive interference
If they beams interfere in a way that makes the total beam less bright, it is called destructive interference.

2. Constructive and Destructive Interference
Two waves (top and middle) arrive at the same point in space.
The total wave amplitude is the sum of the two waves.
The waves can add constructively or destructively

3. Coherence
If the phase of a light wave is well defined at all times the light is said to be coherent.
If the phase of a light wave varies randomly then the light is said to be incoherent.

4. For incoherent light, interference is hard to observe because it is “washed out” by the very rapid phase jumps of the light.

5. Young’s Double Slit Experiment
Interference of light waves was first demonstrated by Thomas Young in 1801.
Illuminated two small slits with coherent light.
Observed a pattern of light and dark regions on a distant screen.

6. Interference of waves from double slit
Each slit acts as a source of an outgoing wave.
The two waves are coherent
The amplitude of the light wave reaching the screen is the sum of the waves coming from the two slits.

7. Interference Fringes

8. Path Difference
We can understand this interference pattern because light from the two apertures will travel a different distance before reaching a point on the screen. The difference in distance is called the path difference. P
Light

9. If the two slits are separated by a distance d and the screen is far away then the path difference at point P is Dl = dsinq
If Dl = l, 2l, 3l, etc, then the waves will arrive in phase and there will be a bright spot on the screen.
Light P q
dsinq

10. Interference Conditions
For constructive interference, the path difference must be zero or an integral multiple of the wavelength:
For destructive interference, the path difference must be an odd multiple of half wavelengths:
m is called the order number

12. Phase of wave reflected by interface between two media

13. Interference in Thin Films
We have all seen the colorful patterns which appear in soap bubbles. The patterns result from an interference of light reflected from both surfaces of the film: t
n>1
180o phase change
0o phase change
2t = ml (m = 0, 1, 2…) Destructive (invisible)
2t = (m + 1/2)l (m = 0, 1, 2…) Constructive (bright color)

14. Soap Film Interference