Question

A green laser beam (550 nm) strikes a grating and creates an interference pattern on a wall 2.0 m away. The first maximum (fringe #1) occurs 11.0 cm from the middle of the central maximum. (a) Determine the distance between successive slits and the number of slits per mm. (b) Now a red laser (630 nm) replaces the green. On which side of the green fringe will the first red fringe appear – closer to the central maximum or further out? Explain. (c) Using the same grating and employing a small angle approximation, how far from the green fringe location will the first red fringe be on the wall?

Answer 1

Wavelength w is 550nm=550*10^-9m, screen distance D is 2 metre and position of first maximum y is 0.11m

so, distance between successive slits is d= wD/y= 10^-5m

And the number of slits per mm is 1000/d= 100

Now all the parameters are same but the wavelength has changed to 630*10^-9m

So, the new position of the first maximum is y= wD/d= 0.126m, and it is further out.

Distance the green fringe location will be from the first red fringe on the wall is 0.126-0.11= 0.016m