In a two-slit experiment, a third-order bright fringe is observed at an angle of $7.10 ^ { \circ }$ away from the centerline. If the wavelength of light is 595 nm, how far apart are the two slits?
A) $2.12 \times 10 ^ { - 5 } \mathrm {~m}$
B) $1.44 \times 10 ^ { - 5 } \mathrm {~m}$
C) $1.07 \times 10 ^ { - 5 } \mathrm {~m}$
D) $2.53 \times 10 ^ { - 5 } \mathrm {~m}$
E) $3.76 \times 10 ^ { - 5 } \mathrm {~m}$

Question

In a two-slit experiment, a third-order bright fringe is observed at an angle of $7.10 ^ { \circ }$ away from the centerline. If the wavelength of light is 595 nm, how far apart are the two slits? 
A) $2.12 \times 10 ^ { - 5 } \mathrm {~m}$
B) $1.44 \times 10 ^ { - 5 } \mathrm {~m}$
C) $1.07 \times 10 ^ { - 5 } \mathrm {~m}$
D) $2.53 \times 10 ^ { - 5 } \mathrm {~m}$
E) $3.76 \times 10 ^ { - 5 } \mathrm {~m}$

Quizplus · Accepted Answer

The distance between the slits in a two-slit experiment can be found using the formula for the position of bright fringes, $d \sin \theta = m\lambda$, where $d$ is the distance between the slits, $\theta$ is the angle of the fringe from the centerline, $m$ is the order of the fringe, and $\lambda$ is the wavelength of the light. Rearranging for $d$, we get $d = \frac{m\lambda}{\sin \theta}$. Substituting $m = 3$, $\lambda = 595 \times 10^{-9} \, \text{m}$, and $\theta = 7.10^\circ$ (converting to radians for the calculation), we find $d \approx 1.44 \times 10^{-5} \, \text{m}$.

In a Two-Slit Experiment, a Third-Order Bright Fringe Is Observed 7.10∘7.10 ^ { \circ }7.10∘

In a Two-Slit Experiment, a Third-Order Bright Fringe Is Observed $7.10 ^ { \circ }$