Question

Two narrow slits emitting light in phase are separated by a distance of 1⋅0 cm. The wavelength of the light is $5·0\times {10}^{-7}\mathrm{m}$. 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

Given:
Separation between two narrow slits, d = 1 cm = 10⁻² m
Wavelength of the light, $\lambda =5\times {10}^{-7}\mathrm{m}$
Distance of the screen, $D=1\mathrm{m}$
(a)
We know that separation between two consecutive maxima = fringe width (β).
That is, $\beta =\frac{\lambda D}{d}$ ...(i)
$$\begin{gathered} =\frac{5\times {10}^{-7}\times 1}{{10}^{-2}}\mathrm{m} \\ =5\times {10}^{-5}\mathrm{m}=0.05\mathrm{mm} \end{gathered}$$

(b)
Separation between two consecutive maxima = fringe width
∴ $\beta =1\mathrm{mm}={10}^{-3}\mathrm{m}$
Let the separation between the sources be 'd'
Using equation (i), we get:
$$\begin{gathered} d\text{'}=\frac{5\times {10}^{-7}\times 1}{{10}^{-3}} \\ \Rightarrow d\text{'}=5\times {10}^{-4}\mathrm{m}=0.50\mathrm{mm}. \end{gathered}$$