Young’s Double SlitContents:

•Interference•Diffraction•Young’s Double Slit

•Angle•Distance

•Single slit•Rayleigh Criterion

Interference

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When the difference in distance (L1- L2) is an integer number of wavelengths (0, 1, 2, 3…) = Constructiveremainder of a half (1/2, 1 1/2, 2 1/2, …) = Destructive

L1 L2

Sources

Young’s Double Slit Experiment

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Monochromatic, coherent lightLight spreads out from slitsScreen has sum of two sourcesInterference pattern on screenDemo

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d = slit separation

Central Maxima

Next Maxima

d

L1

L2

L2 – L1 = d sin

Young’s Double Slit Experiment

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d = slit separationd sin = n (n = 0, 1, 2…) - constructived sin = (n +1/2) - destructive

Central Maxima

Next Maxima

d

L1

L2

L2 - L2 = d sin

Young’s Double Slit Experiment

Young’s Double Slit - Angle1 | 2 | 3 | 4

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d sin = nd = 3.00 x 10-6 m, n = 1, = 6.00o

314 nmW

Two slits are 3.00 x 10-6 m apart. What is the wavelength of the incident light if the bright fringes are separated by 6.00o?

d sin = nd = 9.00 x 10-6 m, n = 3, = 565 x 10-9 m

10.9oW

Two slits are 9.00 x 10-6 m apart. If 565 nm light is incident, what angle separates the central maxima, and the third fringe out?

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Similar triangles - set up proportion s = D d

Central Maxima

Next Maxima

d

L1

Young’s Double Slit Experiment

D

s

Young’s Double Slit Distance1 | 2 | 3 | 4

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d = 2.5 x 10-5 m, D = 5.0 m, = 520 x 10-9 m

.10 mW

520 nm light hits two slits separated by 2.5 x 10-5 m. What distance separates the bright fringes on the screen that is 5.0 m distant?s = D d

d = 2.50 x 10-5 m, D = 5.00 m, d = .0570 m

285 nmW

Light hits two slits separated by 2.50 x 10-5 m. If 5.70 cm separates the bright fringes on the screen that is 5.00 m distant, what is the wavelength of light being used?s = D d

A single slit can make an interference pattern too

Rayleigh Criterion

= 1.22 b

= Angle of resolution (Rad) = Wavelength (m)b = Diameter of circular opening (m)

(Telescope aperture)the bigger the aperture, the smaller the angle you can resolve.

Central maximum of one is over minimum of the other

Rayleigh Criterion1 | 2

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= 1.22 b

= ?, = 550 x 10-9 m, b = 2.54 m = 2.64173E-07

2.6 x 10-7 radians W

What is the angular resolution of the 100 inch (2.54 m) diameter telescope on the top of Mt Wilson? (use 550 nm as the wavelength)(uh 550 nm = 550 x 10-9 m)

= 1.22 b

= 6.00 x 10-7, = 550 x 10-9 m, b = ?b = 1.12 m

1.1 mW

What diameter telescope do you need to resolve two stars that are separated by 1.8 x 1011 m, but are 3.0 × 1017 m from us? (use 550 nm as the wavelength) (AU, 32 LY)

hint = s/r = (1.8 x 1011 m)/(3.0 × 1017 m)