Question

For an interference pattern to be observed between two sources, the emission must be coherent.

i. State the characteristic for the coherent sources.

ii. A light source is directed through two narrow slits separated at 5 x 10 m. Five meters away from the wall is a light detector which detects the interference pattern. It was found that the distance from the central peak to the first order interference fringes was 6 cm. What is the light source's wavelength?

iii. Recommend a suitable modification to the setup so that the distance between two consecutive fringes is increased.

Answer 1

i) The characteristic of the coherent sources: It have the constant phase difference. It have the single frequency. It will have the same amplitude.

ii) As per the question, distance between the slits

$d=5\times 10^{-3}$ m,

Distance between the slits and the wall (D)=5m,

n=1

The distance from the central peak to the first order interference fringes (y)=6cm

let the wavelength of the wave $(\lambda)=?$

$y=\frac{n\lambda D}{d}$

$\Rightarrow \lambda=\frac{dy}{D}$

Now, substituting the values,

$\Rightarrow \lambda =\frac{5\times 10^{-3}\times 6\times 10^{-2}m^2}{5m}=6\times 10^{-5}m$

$\Rightarrow \lambda=60\times 10^{-6}=60\mu m$

iii) we know that, distance between the two consecutive fringes,

$\beta=\frac{\lambda D}{d}$

So, the distance between two slit will get increase if wavelength will get increase.

If D will increase, then distance between the fringe will get increase.

if the distance between the slit will get decrease, then the distance between the slits will get increase.