2. (a) Two narrow slits, illuminated by light consisting of two distinct wavelen

Question

2.

(a) Two narrow slits, illuminated by light consisting of two distinct wavelengths, produce two overlapping colored interference patterns on a distant screen. The center of the eighth bright fringe in one pattern coincides with the center of the fourth bright fringe in the other pattern. What is the ratio of the two wavelengths

(b) A Fraunhofer diffraction pattern of a single slit of width 0.316 mm is produced using light of wavelength 556 nm. Find the angle subtended by the central diffraction maximum.

(c) A monochromatic plane wave of wavelength 510 nm is incident on an opaque screen with a pinhole of diameter 0.103 mm. Find the diameter of the Airy disk on a wall 4.70 m in front of the pinhole.

Explanation / Answer

1)

The formula that govens this is y/L = m(wavelength)/d

Since y, L, and d will be constant in the problem, a ratio can be set up...

m'/wavelength' = m/wavelength

or m'/m = wavelength/wavelength'

That ratio is 8/4 which is 2:1

So your key may want this as 2 or 1/2 which is 0.5

2)

Apply sin(angle) = (wavelength)/a

sin(angle) = (556 X 10-9)/(3.16 X 10-4)

angle = 0.1008o

The total maximum is twice that value, so that would be 0.2016o

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