In a Young's double-slit experiment,by how many wavelengths do the paths from the slits to the screen differ for the m = 3 and the m = 8 minima?
A)10
B)2.5
C)5
D)Some other value than those given since this is for destructive interference.

Question

Quizplus · Accepted Answer

In a Young's double-slit experiment, the path difference between the rays from the two slits to a given point on the screen is given by d sin θ, where d is the slit separation and θ is the angle between the line connecting the slit to the screen and the central axis of the experiment. The minima (destructive interference) occur when the path difference is an odd multiple of half-wavelengths (λ/2, 3λ/2, 5λ/2, etc.). Thus, for the m = 3 minima, the path difference is 3λ/2 - λ/2 = λ, while for the m = 8 minima, the path difference is 8λ/2 - λ/2 = 7λ. The difference in path length between the two is (7λ - λ) = 6λ, which is equivalent to 6 times the wavelength of the light used in the experiment. Therefore, the answer is C) 5.

In a Young's Double-Slit Experiment,by How Many Wavelengths Do the Paths