Answer to Question #103354 in Optics for Aayan kapoor

Question

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

Answer 1

Solution. The distance between slits is 

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

Using the diffraction grating’s slit formula

$$dsin\Theta=m\lambda$$

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

$$sin\Theta \eqslantless 1$$

From the diffraction grating’s formula

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

Therefore the maximum number of principal maxima is equal to 2.

Answer. 2.