Question

What is the longest wavelength that can be observed in the third order for a transmission grating having 5200 slits/cm?

Answer 1

641 nm.

Step-by-step explanation:

Given that,

A transmission grating has 5200 slits/cm.

We need to find the longest wavelength that can be observed in the third order. Using grating equation as follows :

`d\sin\theta=m\lambda` ...(1)

d is slit spacing

No fo slit per unit length :

`N={5200}\ slit/cm\\\\=520000\ slits/m`

We know that, N = 1/d

For longest wavelength, θ = 90°

From equation (1)

`(\sin\theta)/(m\lambda)=(1)/(d)\\\\520000=(\sin(90))/(3\lambda)\\\\\lambda=(1)/(520000* 3)\\\\=6.41* 10^(-7)\ m\\\\=641\ nm`

Hence, the longest wavelength in third order for a transmission grating is 641 nm.