hi the tutors in the library couldnt help me with this so im hoping someone here

Question

hi the tutors in the library couldnt help me with this so im hoping someone here knows how to solve it!! if you could write out your steps and the final answer i would appreciate it!!

In a Young's interference experiment, the two slits are separated by 0.16 mm and the incident light includes two wavelengths: 1 = 540 nm (green) and 2 = 450 nm (blue). The overlapping interference patterns are observed on a screen 1.39 m from the slits.

(a) Find a relationship between the orders m1 and m2 that determines where a bright fringe of the green light coincides with a bright fringe of the blue light. (The order m1 is associated with 1, and m2 is associated with 2.)

m2/m1 = ?

(b) Find the minimum values of m1 and m2 such that the overlapping of the bright fringes will occur and find the position of the overlap on the screen.

m1 = ?
m2 = ?
Distance = ? cm from the central maximum

thank you!!

Explanation / Answer

d = 0.16 mm, L = 1.39 m, 1 = 540 nm (green)2 = 450 nm (blue).
a) overlap: m1*1 = m2*2, so

m2/m1 = 1/2 = 540/450 = 6/5

b) both m1 and m2 must be integers, so minimum value of m1 = 5, m2 = 6

distance = m1*1*L/d = 0.0235 m

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