In a double-slit experiment, the slit separation is $2.0 \mathrm {~mm}$, and two wavelengths, $750 \mathrm {~nm}$ and 900 $\mathrm { nm }$, illuminate the slits. A screen is placed $2.0 \mathrm {~m}$ 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) $4.5 \mathrm {~mm}$
B) $6.0 \mathrm {~mm}$
C) $3.0 \mathrm {~mm}$
D) $1.5 \mathrm {~mm}$

Question

Quizplus · Accepted Answer

For two bright fringes to coincide, their path difference must be an integer multiple of both wavelengths. The path difference is given by $d\sin(\theta) = m\lambda$, where $d$ is the slit separation, $\theta$ is the angle to the fringe, $m$ is the order of the fringe, and $\lambda$ is the wavelength. For small angles, $\sin(\theta) \approx \tan(\theta) = \frac{x}{L}$, where $x$ is the distance from the central maximum and $L$ is the distance to the screen. Setting the path differences equal for both wavelengths and solving for $x$ when they first coincide gives the correct answer.

In a Double-Slit Experiment, the Slit Separation Is 2.0 mm2.0 \mathrm {~mm}2.0 mm

In a Double-Slit Experiment, the Slit Separation Is $2.0 \mathrm {~mm}$