22: Problem 22.6

INTRO:
Light from a sodium lamp (λ=589nm)illuminates two narrow slits. The fringe spacing on a screen 110 cm behind the slits is 3.6mm.

Part A:
What is the spacing (in mm) between the two slits?
Express your answer to two significant figures and include the appropriate units.

SOLUTION:
givens: 
λ = 589 nm = 5.89⋅10^-7 m
L = 110 cm = 1.1 m
Δy = 3.6 mm = 3.6⋅10^-3 m

we can rearrange the formula Δy = λ⋅L/d to give us the distance between the slits, d
d=λ⋅L/Δy → d = (5.89⋅10^-7 m)⋅(1.1 m/3.6⋅10^-3 m) = 1.8⋅10^-4 m = 0.18 mm