Question

Monochromatic light is incident on a grating that is 75 mmwide

and ruled with 50,000 lines. The second-order maximum isseen at
32.5 (degrees). What is the wavelength of theincident light?

Answer 1

Step-by-step explanation:

Given

Grating Width
`w=75 mm`

no of lines
`N=50,000 lines`

inclination of second order maxima
`\theta =32.5^(\circ)`

Condition of maxima For Diffraction grating

`d\sin \theta =m\lambda`

where
`d=Grating\ constant`

`\lambda =wavelength`

`m=order\ of\ maxima`

`d=(width)/(N)`

`d=(75)/(50,000)`

`d=0.0015\ mm`

therefore for second order maxima wavelength of light is given by

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

`\lambda =(0.0015* \sin (32.5))/(2)`

`\lambda =403* 10^(-6)\ m`

`\lambda =403\ nm`