Question

What happens to the distance between maxima when the gratings per mm are increased? How does changing the wavelength of the laser affect the distances between maxima?

Answer 1

For a plane diffraction grating the angular position of maxima is given by,

                $(a+b)\sin \theta =n\lambda$

where, is grating element,distance between two consecutive slits

n is order of maxima and $\lambda$ is wavelength , $\theta$ is the angular separation of maxima

1) If the grating lines per mm is increased, the spacing between the lines decreases thus, grating element decreases.

Now, $\sin \theta$ will increases thus $\theta$ increases. So the distance between maxima increases.

2) If the grating element is fixed and wavength of light of laser is increased, the distance of mxima will increase. If the wavelength of laser light is decreased, then the distance between maxima decreases. So, wavelength is directly proportional to the distance of maxima.

That is why red laser is used with fine grating lines for better view diffraction maxima.