Question

Two lasers are shining on a double slit, with slit separation d. Laser 1has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patterns on a screen a distance 5.00 m away from the slits.

Part A
Which laser has its first maximum closer to the central maximum?

Part B
What is the distance  Δymax-max between the first maxima (on the same side of the central maximum) of the two patterns? Part B.1 Find the location of the first maximum for laser1 Part B.2 Find the location of the first maximum for laser2

Part C
What is the distance  Δymax-min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum? Part C.1Find the location of the second maximum Part C.2Find the value of the third minimum Part C.3Find the location of the third minimum

Answer 1

λ₁ = d/20, λ₂ = d/15, L = 5.00m,
a) y_n = nλL/d
for n = 1, λ₁ < λ₂, soy₁ < y₂ , answer: laser 1
b) Δy₁ = (λ₂ -λ₁)L/d = (1/15 - 1/20)*5.00 m = 8.33 cm
c) second maximum: y₂ = 2λ₁L/d,
third minimum: y₃ = (5/2)λ₂L/d =2.5λ₂L/d
Δy = y₃ - y₂ = (2.5λ₂ -2λ₁)L/d = (2.5/15 - 2/20)L = 0.33 m