Question

Determine the angle for the first order maximum of a 12,000 lines/cm diffraction grating and light wavelength at 550 nm

Answer 1

`\theta=41.29^(\circ)`

Step-by-step explanation:

Given that,

Number of lines,
`N=12000\ lines/cm`

`N=12000* 10^2\ lines/m`

Wavelength,
`\lambda=550\ nm=550* 10^(-9)\ m`

We need to find the angle for the first order maximum, n = 1

`d=(1)/(N)`

`d=(1)/(12000* 10^2)`

`d=8.33* 10^(-7)\ m`

Using the grating equation as :

`d\ sin\theta=n\lambda`

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

`sin\theta=(550* 10^(-9))/(8.33* 10^(-7))`

`\theta=41.29^(\circ)`

So, the angle for the first order maximum is 41.29 degrees. Hence, this is the required solution.