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Physics345
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Homework Statement
a) Explain why a pattern of bright and dark fringes visible on a screen when a light is shone through a double slit.
b) Upon using Thomas Young's double-slit experiment to obtain measurements, the following data were obtained. use this data to determine the wavelength of light being used to create the interference pattern. do this in three different ways.
Homework Equations
mλ=d sinθ
mλ=dxm/L
∆x=Lλ/d
The Attempt at a Solution
a)
When the wave encounters a barrier such as a slit it spreads out into two dimensions causing diffraction, when using a double slit there is going to be two waves that will overlap, since the light passes through two barriers (the double slits). When the overlapping occurs, there will be regions where they overlap constructively. Constructive interference occurs when peaks line up over peaks or valleys over valleys causing waves that are in phase, creating the bright fringes on the screen in the directions of the constructive interference. Where they overlap destructively you get a dark fringe. Destructive interference on the other hand occurs when peaks match up with the valleys and in between them there is a destructive point, creating dark fringes on the screen in the directions of the destructive interference.
https://www.khanacademy.org/science...e-of-light-waves/v/youngs-double-split-part-1
b)
b)
θ=1.12°
m=8
L=302cm=3.02m
4∆x=2.95 / 4
∆x=0.7375 cm=0.0007375m
∆x=7.375 × 10^-4 m
x_4=2.95 × 10^-2 m
d=2.5 ×1 0^-4 m
Method 1:
mλ=d sinθ
λ=(d sinθ)/m
λ=(2.5×10^-4)(sin1.12°) / 8
λ=6.11×10^-7
λ=611 nm
Method 2: do calculations here
mλ=dxm/L
λ=dxm/mL
λ=(2.95×10^-2)(7.375×10^-4) / (4(3.02))
λ=6.11×10^-7
λ=611 nm
Method 3:
∆x=Lλ/d
λ=d∆x/L
λ=(2.5×10^-4 )(7.375×10^-4 ) / 3.02
λ=6.11×10^-7
λ=611 nm
Therefore the wavelength of light being used is 611 nm