Question

Write any two necessary conditions for interference of light. Obtain an expression for fringe width in Young's double slit experiment. Draw curve for intensity distribution in Young's double slit experiment.

Answer 1

1)Light should be propagate in same direction
2)Light should be coherent lights.
=$\Delta S_1{S}_{2}M$
=$\sin \theta =\frac{S_{2}M}{d}$
=$\theta =\frac{S_{2}M}{d}$
=$\Delta O{O}_{1}P$
=$\tan \theta =\frac{X_n}{D}$
=$\theta =\frac{X_n}{D}$
=$\frac{S_{2}M}{d}=\frac{X_n}{D}$
=$S_{2}M=\frac{X_n}{D}\cdot d$
=$\frac{X_n}{D}=n\lambda$
=$X_n=\frac{n_{2}D}{d}$
For dark fringe width $\left({\beta }_{dark}\right)$
=${\beta }_{dark}=X_{n+1}-X_n$
=$X_{n+1}-X_n$
=$(n+1)\frac{\lambda D}{d}-\frac{n\lambda D}{d}$
=$\frac{\lambda D}{d}(n+1-n)$
=${\beta }_{dark}=\frac{\lambda D}{d}$
=For bright fringe width $\left({\beta }_{Bright}\right)$:
=$\frac{X_{nd}}{D}=(2n+1)\frac{\lambda }{2}$
=${\beta }_{Bright}=X_{n+1}-X_n$
=${\beta }_{Bright}=\left(2\right(n+1)+1)\frac{\lambda D}{2d}-(2n+1)\frac{\lambda D}{2d}$
=$\frac{\lambda D}{2d}(2n+2+1-2n-1)$
=$\frac{\lambda D}{2d}\cdot 2$
=${\beta }_{Bright}=\frac{\lambda D}{d}$