Answer to Question #125456 in Electricity and Magnetism for hx

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.