Question

The fringe width (β) of a diffraction pattern and the slit width d are related as:​

Answer 1

Answer:

We know the fringe width β=

d

Dλ

whereD= distance between slits and screen

λ= wavelength of light used

d= distance between two slits

by above formula β∝

d

1

therefore fringe width increases when distance between two slits will decrease or we can say that we move the slits closer together.

Answer 2

Relation between fringe width (β) and slit width (d) :

• Fringe width is the separation between adjacent bright fringe or adjacent dark fringe in YDSE experiment.

• $\lambda$ is wavelength, D is distance of screen from slit and d is slit width.

• So, let's fInd out the separation between $n^{th}$ and $(n+1)^{th}$ bright fringe.

$\therefore \: \beta = r_{n + 1} - r_{n}$

$\implies \: \beta = \dfrac{(n + 1) \lambda D}{d} - \dfrac{n \lambda D}{d}$

$\implies \: \beta = \dfrac{(n + 1 - n) \lambda D}{d}$

$\implies \: \beta = \dfrac{\lambda D}{d}$

So, value of fringe width is $\boxed{\beta=\lambda D/d}$