Question

Two narrow slits emitting light in phase are separated by a distance of 1⋅0 cm. The wavelength of the light is 5·0×10-7 m. The interference pattern is observed on a screen placed at a distance of 1⋅0 m. (a) Find the separation between consecutive maxima. Can you expect to distinguish between these maxima? (b) Find the separation between the sources which will give a separation of 1⋅0 mm between consecutive maxima.

Answer 1

(a) The separation between consecutive maxima and distinguish between these maxima is $0.05 \mathrm{mm}$

(b) The separation between the sources which will give a separation of 1⋅0 mm between consecutive maxima is $0.50 \mathrm{mm}$

Explanation:

Separation of two small slits, $d=1 \mathrm{cm}=10-2 \mathrm{m}$

The light wavelength

$\lambda=5 \times 10-7 \mathrm{m}$ screen distance

$D=1 \mathrm{m}$

(a) The spacing between two successive maxima is equal to the width of the fringe.

We know that the difference between two successive maxima =  fringe width (β).

That is,

$\beta=\frac{\lambda D}{d} \ldots(i)$

$=\frac{5 \times 10^{-7}}{10^{-2}} m=5 \times 10^{-5} m=0.05 m m$

(b)  Separating between two consecutive maxima = width of the fringe

$B=1 \mathrm{mm}=10-3 \mathrm{m}$

Let the source-separation be 'd '

Use of Equation (i), we get:

$d^{\prime}=\frac{5 \times 10^{-7}}{10^{-2}}$

$\Rightarrow d^{\prime}=5 \times 10^{-4} \mathrm{m}=0.50 \mathrm{mm}$