Interference of Light Waves and Young’s Experiment

Interference is the redistribution of light intensity that occurs when two light waves overlap. Young's double-slit experiment gave strong evidence for the wave nature of light by producing alternate bright and dark fringes on a screen.

Ordinary light sources do not give stable fringes

• Ordinary sources emit light independently, so their phase difference changes randomly.
• Because of this random phase variation, sustained interference fringes are not observed.
• To obtain a clear interference pattern, two coherent sources are required.

Interference is the phenomenon in which light intensity is modified due to the superposition of two or more light waves.

A fringe is a bright or dark band formed on the screen due to constructive or destructive interference.

Fringe width is the distance between two consecutive bright fringes or two consecutive dark fringes.

\[\alpha=\frac{\beta}{D}=\frac{\lambda}{d}\]

\[\begin{array} {c}x_n=\frac{n\lambda D}{d}=n\beta \end{array}\]

\[\begin{array} {cc} & x_m=\frac{(2m-1)\lambda D}{2d} \end{array}\]

\[\beta=\frac{\lambda D}{d}\]

\[x_n-x_m=\left[n-\frac{(2m-1)}{2}\right]\beta\]

Experimental Arrangement

In Young's experiment, light from a single source first falls on two closely spaced narrow slits, usually denoted by S1 and S2. Since both slits receive light from the same parent source, they act as coherent sources.

A screen is placed at a distance from the slits, and alternate bright and dark bands are observed on it. This pattern is called the interference pattern.

Diagram suggestion

Use a labelled diagram showing:

• source S
• two narrow slits S1 and S2
• slit separation d
• screen at distance D
• central bright fringe at O
• a general point P on the screen
• path difference between waves reaching P

When light waves from S1 and S2 reach a point on the screen, they combine by superposition. Depending on their phase relation, the resultant intensity may increase or decrease.

Constructive Interference

Bright fringes are formed when the path difference between the two waves is an integral multiple of wavelength.

where n = 0, 1, 2, 3, ...

Destructive Interference

Dark fringes are formed when the path difference is an odd multiple of half a wavelength.

where m = 1, 2, 3, ...

Let:

• wavelength of light = λ
• distance between slits = d
• distance of screen from slits = D
• distance of fringe from central bright fringe = x

For small angles, the path difference at a point P on the screen is approximately:

Position of Bright Fringe

For constructive interference: \[\frac {dx_n}{D}\]

Therefore,

where n = 0, 1, 2, 3, ...

Position of Dark Fringe

For destructive interference:

Therefore,

where m = 1, 2, 3, ...

Fringe width is the distance between two successive bright fringes or two successive dark fringes.

Angular Fringe Width

These expressions show that fringe width increases with wavelength and screen distance, but decreases when slit separation increases.