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.

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

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.

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

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.

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.

Interference Fringes

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

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

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

Phase of wave reflected by interface between two media

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)

Soap Film Interference