Question

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

Answer 1

Answer:

641 nm.

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)

$\dfrac{\sin\theta}{m\lambda}=\dfrac{1}{d}\\\\520000=\dfrac{\sin(90)}{3\lambda}\\\\\lambda=\dfrac{1}{520000\times 3}\\\\=6.41\times 10^{-7}\ m\\\\=641\ nm$

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