An optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is $1.70 \mathrm {~m}$ from the slits. If the slits are illuminated with coherent light of wavelength 633 nm, how far apart should the slits be?
A)68.5 ?m
B)74.0 ?m
C)79.5 ?m
D)63.0 ?m

Question

Quizplus · Accepted Answer

The distance between bright fringes in a double-slit experiment is given by $ \Delta y = \frac{\lambda L}{d} $. Solving for $d$, we have $d = \frac{\lambda L}{\Delta y}$. Substituting $\lambda = 633 \times 10^{-9} \, \text{m}$, $L = 1.70 \, \text{m}$, and $\Delta y = 15.7 \times 10^{-3} \, \text{m}$, we find $d \approx 68.5 \, \mu\text{m}$.

An Optical Engineer Needs to Ensure That the Bright Fringes 1.70 m1.70 \mathrm {~m}1.70 m

An Optical Engineer Needs to Ensure That the Bright Fringes $1.70 \mathrm {~m}$