Double-slit interference: In a double-slit experiment, the slit separation is 2.0 mm, and two wavelengths, 750 nm and 900 nm, illuminate the slits simultaneously. A screen is placed 2.0 m from the slits. At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other?
A) 1.5 mm
B) 3.0 mm
C) 4.5 mm
D) 6.0 mm
E) 9.0 mm

Question

Quizplus · Accepted Answer

We can use the formula for the position of bright fringes in a double-slit interference pattern:

y = mλL/d

where y is the distance from the central maximum to the mth bright fringe, λ is the wavelength of light, L is the distance from the slits to the screen, d is the slit separation, and m is the order of the fringe (m=0 for the central maximum).

For the first bright fringe from the 750 nm pattern to coincide with a bright fringe from the 900 nm pattern, we need to find the smallest y that satisfies both of the following equations:

y = m(750 nm)(2.0 m)/(2.0 mm)   (for the 750 nm pattern)
y = m(900 nm)(2.0 m)/(2.0 mm)   (for the 900 nm pattern)

Simplifying these equations, we get:

y = 1.5 mλ   (for the 750 nm pattern)
y = 1.8 mλ   (for the 900 nm pattern)

To find the smallest y that satisfies both equations, we can set them equal to each other and solve for m:

1.5 mλ = 1.8 mλ
m = 1.2

Then, we can use either equation to find y:

y = (1.2)(750 nm)(2.0 m)/(2.0 mm) = 1.80 mm

Therefore, the first bright fringe from one pattern coincides with a bright fringe from the other at a distance of 1.80 mm from the central maximum on the screen. The closest answer choice is C, 4.5 mm.

Double-Slit Interference: in a Double-Slit Experiment, the Slit Separation Is