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 ${~m}$ 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 μm
B) 74.0 μm
C) 79.5 μm
D) 63.0 μm

Question

Quizplus · Accepted Answer

The distance between bright fringes in a double-slit experiment is given by:$$d=\frac{\lambda D}{d}$$where:* d is the distance between the slits* $\lambda$ is the wavelength of light* D is the distance between the slits and the detectorIn this problem, we are given:* D = 1.70 m* $\lambda$ = 633 nm = 633 x 10^-9 m* d = 15.7 mm = 15.7 x 10^-3 mSolving for d, we get:$$d=\frac{\lambda D}{d}=\frac{(633\times10^{-9}\text{ m})(1.70\text{ m})}{15.7\times10^{-3}\text{ m}}=\boxed{68.5\times10^{-6}\text{ m}}$$

An Optical Engineer Needs to Ensure That the Bright Fringes m{~m} m

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