Question

If the incident beam falls normally on the double-slit apparatus, find the order of the interference minima on the screen.

• A. Only the first order minima are possible
• B. Only the first and second order minima are possible
• C. Total six minima appear on the screen
• D. Total eight minima appear on the screen

Answer 1

The correct option is B Only the first and second order minima are possible

Path difference between the light reaching the point P via $S_{1}Pand{S}_{2}P$, $\Delta x=dsin\theta$

For minima, $\Delta x=(n+\frac{1}{2})\lambda$

Thus, $dsin\theta =(n+\frac{1}{2})\lambda$

Given:$d=1mm\lambda =.5mm$

$⟹sin\theta =(n+\frac{1}{2})\frac{1}{2}$

But $0\le sin\theta \le 1$

Thus $n=0and1$ only satisfies the relation.

Hence there will be first and second order minima and total number of minima be observed is 4.