Question

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

Given

Separation between two narrow slits, d = 1 cm = 10⁻² m

Wavelength of the light,

\[\lambda = 5 \times  {10}^{- 7}   m\]

Distance of the screen,

\[D = 1  m\]

(a)

We know that separation between two consecutive maxima =  fringe width (β).

That is,

\[\beta = \frac{\lambda D}{d}............(1)\]

\[= \frac{5 \times {10}^{- 7} \times 1}{{10}^{- 2}}  m\]

\[   = 5 \times  {10}^{- 5}   m = 0 . 05 mm\]

(b)

Separation between two consecutive maxima = fringe width

\[\therefore\beta = 1  mm =  {10}^{- 3}   m\]

Let the separation between the sources be 'd'

Using equation (1), we get

\[d' = \frac{5 \times {10}^{- 7} \times 1}{{10}^{- 3}}\]

\[ \Rightarrow d' = 5 \times  {10}^{- 4}   m = 0 . 50  mm.\]