Question

Two coherent plane light waves of equal amplitude makes a small angle α(<<1) with each other. They fall almost normally on a screen. If $\lambda$ is the wavelength of light waves, the fringe width Δx of interference patterns of the two sets of wave on the screen is

Answer 1

Solution:

The fringe seperation for a double slit(2 coherent sources) is given by;

$Y=\frac{\lambda D}{a}$

D= distance between slit and screen

a= seperation of sources slit

For wavefront meeting at the screen with a seperation angle $\alpha$ ,

$sin\alpha \approx \frac{a}{D}$

or we can write it;

$\frac{1}{sin\alpha }=\frac{D}{a}$

$Y=\frac{\lambda }{sin\alpha }$

For small angle,

$sin\alpha \approx \alpha$

$Y=\frac{\lambda }{\alpha }$

So, fringe width Δx of interference patterns of the two sets of wave on the screen is:

$\frac{\lambda }{a}$