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

Solution. The distance between slits is 

$$d=\frac {1cm}{10000}=10^{-4}cm=10^{-6}m$$

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

$$d sin\theta =m\lambda$$

where Θ is angle between normal and maximum direction; m is number of principal maxima; λ=487nm is wavelength. Therefore

$$m=\frac{d sin\theta}{\lambda}$$

Using the properties of sine function

$$sin\theta \eqslantless 1$$

Hense

$$m\eqslantless\frac{d }{\lambda}$$

$$\frac{d }{\lambda} =\frac{10^{-6}}{487\times 10^{-9}}=2.053$$

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

Answer. 2.