As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.01 mm apart and position your screen 3.65 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 641 nm. How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe? Express your answers in millimeters.

Question

Physics

Merle

6 March, 14:04

As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.01 mm apart and position your screen 3.65 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 641 nm. How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe? Express your answers in millimeters.

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Answers (1)

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Daffodil · Answer 1

2.316e-3 and 3.47e-3

Explanation:

Now, at that angle, we look at the bright spots on the screen.

tan θ = x / L (x is the horizontal distance from the centre of the screen, L is distance to screen)

For small angles, we can approximate that tan θ = sin θ.

nλ / d = x / L so then x = n λ L / d

First bright fringe, n = 1

x = (1) (641*10^-9 m) (3.65 m) / (1.01*10^-3 m) = 2.316e-3

For destructive interference (dark fringes), equation becomes:

x = (n - 0.5) λ L / d

Second dark fringe, n = 1.5

x = 1.5 (641*10^-9 m) (3.65 m) / (1.01*10^-3 m) = 3.47e-3