Question

State two conditions for sustained interference of light. Also write the expression for the fringe width

Answer 1

Conditions for sustained interference pattern:

1. The two sources of light must be coherent with same frequency or wavelength and with same phase or constant phase difference.

2. The two sources should preferably have the same amplitude.

3. The two sources must be very close to each other.

4. The sources should emit light waves continuously.

From YDSE,

$\Delta x=\frac{yd}{D}$

$\lambda (n-\frac{1}{4})=\frac{yd}{D}$

$n=1,\lambda (1-\frac{1}{4})=\frac{y_{1}d}{D}$

$\frac{3\lambda }{4}=\frac{y_{1}d}{D}$

$y_1=\frac{3\lambda D}{4d}$

$n=2,\lambda (2-\frac{1}{4})=\frac{y_{2}d}{D}$

$\frac{7\lambda }{4}=\frac{y_{2}d}{D}$

$y_2=\frac{7\lambda D}{4d}$

Fringe width, $\beta =y_2-y_1$

$\beta =\frac{7\lambda D}{4d}-\frac{3\lambda D}{4d}$

$\therefore \beta =\frac{\lambda D}{d}$