Two thin slits are $6.00 \mu \mathrm { m }$ apart. Monochromatic coherent light falls on these slits, and produces a fifth-order bright interference fringe at an angle of $32.3 ^ { \circ }$ away from the centerline. What is the wavelength of the light?
A) $164 \mathrm {~nm}$
B) $416 \mathrm {~nm}$
C) $641 \mathrm {~nm}$
D) $614 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The wavelength of the light can be calculated using the formula for the angle of the m-th order bright fringe in a double-slit interference pattern: $d \sin \theta = m \lambda$. Here, $d = 6.00 \mu m = 6.00 \times 10^{-6} m$, $\theta = 32.3^\circ$, and $m = 5$. Solving for $\lambda$, we get $\lambda = \frac{d \sin \theta}{m} = \frac{6.00 \times 10^{-6} \times \sin(32.3^\circ)}{5} \approx 641 \mathrm{~nm}$.

Two Thin Slits Are 6.00μm6.00 \mu \mathrm { m }6.00μm Apart Monochromatic Coherent Light Falls on These Slits, and Produces

Two Thin Slits Are $6.00 \mu \mathrm { m }$ Apart Monochromatic Coherent Light Falls on These Slits, and Produces