Question

Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on a diffraction grating with 500 lines/mm.

Answer 1

60.46°

Step-by-step explanation:

Given that, the wavelength of yellow light which is falling on grating is,

`\lambda=580 nm\\\lambda=580* 10^(-9)m`

The angle is of the order of 3 means m=3.

And number of lines per mm is,

`N=500(lines)/(mm)\\N=(500* 10^(3))(lines)/(m)`

Therefore the condition of maxima,

`m\lambda=dsin\theta`

Here,
`d=(1)/(N)`

And for third order maxima, m=3

`3\lambda=(1)/(N) sin\theta\\sin\theta=3 \lambda N`

Therefore,

`sin\theta=3* 580* 10^(-9)m* 500* 10^(3)m\\sin\theta=0.87\\\theta=sin^(-1) (0.87)\\\theta=60.46^(\circ)`

Therefore, the angle for third order maxima is 60.46°.