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As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.15 mm apart and position your screen
Question
As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.15 mm apart and position your screen 3.93 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 647 nm . How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe
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Physics
3 years
2021-09-05T02:12:56+00:00
2021-09-05T02:12:56+00:00 1 Answers
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Answer:
a) y = 2.21 10⁻³ m, b) y = 5.528 10⁻³ m
Explanation:
In the double-slit experiment the interferences occur at the positions
d sin θ = m λ constructive interference
d sin θ = (m + ½) λ destructive interference
let’s use trigonometry for the angle
tan θ = y / L
as in this experiment the angles are very small
tan θ = sin θ/cos θ = sin θ
sin θ = y / L
we substitute
d y / L = m λ constructive interference
d y / L = (m + ½) λ destructive interference
Let’s answer the questions
a) first line of constructive interference me = 1
y = m λ L / d
y = 1 647 10⁻⁹ 3.93 /1.15 10⁻³
y = 2.21 10⁻³ m
b) second dark band m = 2
y = (m + ½) λ L / d
y = (2 + ½) 647 10⁻⁹ 3.93 /1.15 10⁻³
y = 5.528 10⁻³ m