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
[tex]d=\dfrac{1}{N}[/tex]
[tex]d=\dfrac{1}{355\times10^{-3}}[/tex]
[tex]d=2.816\times10^{-6}\ m[/tex]
We need to calculate the angle
Using formula of distance
[tex]y=D\tan\theta[/tex]
[tex]\thata=\tan^{-1}(\dfrac{y}{D})[/tex]
Put the value into the formula
[tex]\theta= \tan^{-1}(\dfrac{0.164}{1.2})[/tex]
[tex]\theta=7.78^{\circ}[/tex]
We need to calculate the wave length
Using formula of wavelength
[tex]d\sin\theta=m\lambda[/tex]
[tex]\lambda=\dfrac{d\sin\theta}{m}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{2.816\times10^{-6}}{1}\sin7.78[/tex]
[tex]\lambda=381\ nm[/tex]
Hence, The wavelength of light is 381 nm.
