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# double-slit interference

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1. Blue light at 480nm impinges perpendicularly on a pair of very narrow parallel slit apertures separated by 0:15mm. A fringe pattern appears on a screen 2m away. How far (in mm) from the central axis on either side will we find the second-order (m = 2) bright bands?

2. Red plane waves from a ruby laser (lambda= 694.3nm) in air impinge on two parallel slits in an opaque screen. A fringe pattern forms on a distant wall, and we see the fourth bright band 1 degree above the central axis. Calculate the separation between the slits (in mm).

3. Parallel rays of blue light from an argon ion laser (lambda = 487.99nm) are incident on a screen containing two very narrow slits separated by 0:2mm. A fringe pattern appears on a sheet of film held 1m away. How far (in mm) from the central axis is the fourth maximum?

https://brainmass.com/physics/optics/double-slit-interference-209559

## SOLUTION This solution is FREE courtesy of BrainMass!

Please see the attached file for detailed solution.

For the double-slit interference, the constructive interference (bright fringe) occurs when:

Where m is the order of the maximum observed,
x is the distance between the bands of the light and the center maximum (fringe distance),
L is the distance from the slits to the screen centerpoint,
d is the separation of the slits, and
λ is the wavelength of the light.

Physical optics (Interference)
1. Blue light at 480nm impinges perpendicularly on a pair of very narrow parallel slit apertures separated by 0:15mm. A fringe pattern appears on a screen 2m away. How far (in mm) from the central axis on either side will we find the second-order (m = 2) bright bands?
m = 2, λ = 480 nm = 480 * 10-9 m, d = 0.15 mm = 0.15 * 10-3 m, and L = 2 m
So

Thus, the second-order bright bands are 12.8 mm from the central axis on either side.

2. Red plane waves from a ruby laser (lambda= 694.3nm) in air impinge on two parallel slits in an opaque screen. A fringe pattern forms on a distant wall, and we see the fourth bright band 1 degree above the central axis. Calculate the separation between the slits (in mm).

Using the small angle approximation,

Then

So the separation between the slits is 0.159 mm.

3. Parallel rays of blue light from an argon ion laser (lambda = 487.99nm) are incident on a screen containing two very narrow slits separated by 0:2mm. A fringe pattern appears on a sheet of film held 1m away. How far (in mm) from the central axis is the fourth maximum?
d = 0.2 mm, L = 1 m, m = 4, λ = 487.99 mm

The fourth maximum is 9.76 mm away from the central axis.

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