Question

A diffraction grating with 355 lines/mm is 1.2 m in front of a screen. What is the wavelength of light whose first-order maxima will be 16.4 cm from the central maximum on the screen?

Answer 1

Answer:

The wavelength of light is 381 nm.

Explanation:

Given that,

Distance of screen D= 1.2 m

Diffraction grating = 355 lines/mm

Order m= first

Distance from the central maximum on the screen y= 16.5 cm

We need to calculate the width of slits

$d=\dfrac{1}{N}$

$d=\dfrac{1}{355\times10^{-3}}$

$d=2.816\times10^{-6}\ m$

We need to calculate the angle

Using formula of distance

$y=D\tan\theta$

$\thata=\tan^{-1}(\dfrac{y}{D})$

Put the value into the formula

$\theta= \tan^{-1}(\dfrac{0.164}{1.2})$

$\theta=7.78^{\circ}$

We need to calculate the wave length

Using formula of wavelength

$d\sin\theta=m\lambda$

$\lambda=\dfrac{d\sin\theta}{m}$

Put the value into the formula

$\lambda=\dfrac{2.816\times10^{-6}}{1}\sin7.78$

$\lambda=381\ nm$

Hence, The wavelength of light is 381 nm.