Question

You and a friend are running some physics experiments to test the wave nature of light. To do so, you cut two very narrow slits on a black plastic sheet, separated by 0.150 mm, and shine coherent light from a laser pointer through them. According to the label on your friend’s laser pointer, it emits coherent light at 570 nm, while your laser pointer doesn’t have any information about the wavelength of light emitted. You then observe their respective interference patterns on a distant screen 4.00 m from the slits and you notice that your laser is creating a narrower pattern than your friend’s. If the distance on the screen between the first-order bright fringes of the two lasers is 3.20 mm, what is the wavelength of light emitted by your laser?

Answer 1

given
slit seperation, d = 0.15 mm = 0.15*10^-3 m
lamda1 = 570 nm
distance between slits and screen, R = 4.00 m

As your laser is creating a narrower pattern than your friend’s, your lase wavelength must be smaller than your friends' laser wavelength.

let lamda2 is the wavelength of your laser.

y1_max(lamda1) - y1_max*(lamda2) = lmada1*R/d - lmada2*R/d

3.20*10^-3 = (lamda1 - lamda2)*R/d

3.20*10^-3*d/R = lamda1 - lamda2

==> lamda2 = lamda1 - 3.20*10^-3*d/(R)

= 570*10^-9 - 3.2*10^-3*0.15*10^-3/4

= 4.50*10^-7 m (or) 450 nm <<<<<<<------------------Answer