Answer to Question #202099 in Optics for prachi

Question

A grating has 10,000 lines per cm. What is the maximum number of principal  maxima that can be formed for light of wavelength 5×10^-5 cm?

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

$m\eqslantless\frac{d }{\lambda}$ $\frac{d }{\lambda} =\frac{10^{-6}}{5\times 10^{-7}}=2$

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

Answer. 2.