Question

A diffraction grating that has 4500 lines/cm is illuminated by light that has a single wavelength. If a second order maximum is observed at an angle of 42° with respect to the central maximum, what is the wavelength of this light?

Answer 1

The wavelength is 742.7 nm.

Step-by-step explanation:

Given that,

Grating = 4500 lines/cm

Angle = 42°

Order number =2

We need to calculate the distance

`d=(1*10^(-2))/(4500)`

`d=2.22*10^(-6)\ m`

We need to calculate the wavelength

Using diffraction formula

`d\sin\theta=m*\lambda`

`\lambda=(d\sin\theta)/(m)`

`\lambda=(2.22*10^(-6)*\sin42)/(2)`

`\lambda=7.427*10^(-7)`

`\lambda=742.7\ nm`

Hence, The wavelength is 742.7 nm.