Name: Brewster’s Law
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: Light is a transverse electromagnetic wave with electric field vectors vibrating in infinite directions perpendicular to the direction of propagation. Let's...

Question

Assuming the expression for the path difference between two waves meeting at a point on the screen, obtain an expression for the fringe width in Young’s double slit experiment.

When are two sources of light said to be coherent ?

Accepted Answer

The expression for path difference between two waves meeting at a point on the screen: $\frac{x d}{D}$

Here, $x$ is the distance between the fringe and the central maxima, $d$ is the separation between the two coherent sources, $D$ is the distance between coherent sources and the screen and $λ$ is the wavelength of the wave emitted by the coherent source.

When the fringe is bright then $\frac{x_{n} d}{D} = n λ$

When the fringe is dark then $\frac{x_{n} d}{D} = (2 n + 1) \frac{λ}{2}$

Assuming two consecutive bright fringes: $x_{n}$ and $x_{n + 1}$ . The separation between these two fringes will give fringe width:

$x_{n + 1} - x_{n} = \frac{(n + 1) λ D}{d} - \frac{n λ D}{d} = \frac{λ D}{d}$

Hence, the expression for fringe width is $\frac{λ D}{d}$ .

Two sources are said to be coherent when the wavelength of the light emitted by the sources are identical and they are of identical phases (i.e. the phase difference between the two waves is zero).

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