Question

Find the slit spacing of a diffraction grating necessary for 450 nm light to have a first-order (m=1) principal maximum at 15⁰.

Answer 1

The slit spacing of a diffraction grating necessary for 450 nm light to have a first-order (m=1) is calculated using the formula as given below:

d=(m λ)/sin900---(1)

here d is slit spacing and λ is the wavelength,m=1( as it is first-order), and angle is 900 for principal maxima at 150.

using the above data values in equation (1), and hence on solving further solving we get the values as below:

d=(1*450)

i.e d=450 nm

Which means the slit spacing of a diffraction grating necessary for 450 nm light to have a first-order (m=1) is equal to 450 nm.