Question

A grating has 10,000 lines per cm. Calculate the maximum number of principal maxima that can be formed for light of wavelength 487 nm.

Answer 1

The distance between slits is $\dfrac{1}{10000}=10^{-4}cm=10^{-6}cm$

Once a value for the diffraction grating’s slit spacing d has been determined, the angles for the sharp lines can be found using the equation

$dsin\theta=m\lambda$

where $\theta$ is angle between normal and maximum direction; m is number of principal maxima;

λ=487nm is wavelength. Therefore

$m=dsin\theta/\lambda$

Using the properties of sine function

$sinθ⪕1$

Hence

$m⪕ ​ \dfrac{d }{\lambda} =\dfrac{10^{-6}}{487\times 10^{-9}}=2.053 ​$

As result get the maximum number of principal maxima is equal to 2.