A pair of narrow slits that are $1.8 \mathrm {~mm}$ apart is illuminated by a monochromatic coherent light source. A fringe pattern is observed on a screen $4.8 \mathrm {~m}$ from the slits. If there are $5.0$ bright fringes/cm on the screen, what is the wavelength of the monochromatic light?
A) $750 \mathrm {~nm}$
B) $600 \mathrm {~nm}$
C) $650 \mathrm {~nm}$
D) $700 \mathrm {~nm}$
E) $550 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The distance between bright fringes is given by:$$d\sin\theta=m\lambda$$where $d$ is the distance between the slits, $\theta$ is the angle of the bright fringe from the central fringe, $m$ is the order of the bright fringe, and $\lambda$ is the wavelength of the light.In this case, we have $d=1.8 \mathrm {~mm}$, $L=4.8 \mathrm {~m}$, and $m=5$. We can use the small angle approximation $\sin\theta\approx\tan\theta\approx\theta$ to get:$$\theta=\frac{my}{L}=\frac{(5)(1 \mathrm {~cm})}{480 \mathrm {~cm}}=0.0104 \mathrm {~rad}$$Substituting this into the first equation, we get:$$1.8 \mathrm {~mm}\times 0.0104 \mathrm {~rad}=5\lambda$$$$\lambda=\frac{1.8 \mathrm {~mm}\times 0.0104 \mathrm {~rad}}{5}=3.74 \times 10^{-5} \mathrm {~m}=374 \mathrm {~nm}$$This is closest to choice A, $750 \mathrm {~nm}$.

A Pair of Narrow Slits That Are 1.8 mm1.8 \mathrm {~mm}1.8 mm Apart Is Illuminated by a Monochromatic Coherent Light Source

A Pair of Narrow Slits That Are $1.8 \mathrm {~mm}$ Apart Is Illuminated by a Monochromatic Coherent Light Source