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

Question

Quizplus · Accepted Answer

The distance between bright fringes in a double-slit experiment is given by the formula $y = \frac{\lambda L}{d}$, where $y$ is the fringe separation, $\lambda$ is the wavelength of the light, $L$ is the distance from the slits to the screen, and $d$ is the distance between the slits. Rearranging this formula to solve for $d$, we get $d = \frac{\lambda L}{y}$. Substituting the given values ($\lambda = 633 \times 10^{-9} \, \text{m}$, $L = 1.70 \, \text{m}$, and $y = 15.7 \times 10^{-3} \, \text{m}$), we find $d \approx 68.5 \, \mu\text{m}$.

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