Question

Find the maximum number of lines per centimeter a diffraction grating can have and produce a first-order maximum for the largest wavelength of visible light. (Assume the wavelengths of visible light range from 380 nm to 760 nm in a vacuum.)

Answer 1

To solve this problem it is necessary to apply the concepts related to constructive interference for multiple split.

The precaution is given by,

$dsin\theta = m\lambda$

Where,

d = Distance between the slits

$\theta =$ Angle between the path and a line from the slits to the screen

m = Any integer, representing the number of repetition of the spectrum.

$\lambda =$Wavelength

For first order equation we have that m = 1 then

$d sin\theta = \lambda$

As the maximum number of lines corresponds to the smallest d values, we have that $\theta = 90$

$d sin90=\lambda$

$d = 760nm$

Therefore the maximum numbers of lines per centimeter would be

$N = \frac{10^{-2}m}{d}$

$N = \frac{10^{-2}m}{760*10^{-9}m}$

$N = 13157.89$

The maximum numbers of lines per centimeter is 13158