Question

A helium-neon laser (λ=633nm) illuminates a diffraction grating. The distance between the two m=1 bright fringes is 35 cm on a screen 2.5 m behind the grating.

What is the spacing between slits of the grating?

Answer 1

Answer:

$9.07443\times 10^{-6}\ m$

Explanation:

d = Spacing between slits of the grating

$\lambda$ = Wavelength = 633 nm

As there are two bright fringes they will equally dispose on the screen from the central point

$\dfrac{0.35}{2}=0.175\ m$

We have the relation

$tan\theta=\dfrac{0.175}{2.5}\\\Rightarrow \theta=tan^{-1}\dfrac{0.175}{2.5}\\\Rightarrow \theta=4^{\circ}$

Wavelength is given by

$\lambda=dsin\theta\\\Rightarrow d=\dfrac{\lambda}{sin\theta}\\\Rightarrow d=\dfrac{633\times 10^{-9}}{sin4}\\\Rightarrow d=9.07443\times 10^{-6}\ m$

The spacing between slits of the grating is $9.07443\times 10^{-6}\ m$