# Diffraction from a Single Slit

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Diffraction from a Single Slit

Thought Question Consider a single slit diffraction pattern. At the first dark fringe above the middle bright fringe, what is the phase difference between the contribution to the field from the topmost and bottommost edges of the slit? A : 45 degrees B : 90 degrees C : 180 degrees D : 360 degrees E : None of the above

If we half the slit width, the central bright fringe
Becomes wider Remains the same Becomes narrower

Light impinges on a single slit but suffers no significant diffraction
Light impinges on a single slit but suffers no significant diffraction. We conclude that the wavelength of the light is much shorter than the slit width. much longer than the slit width. c. on the order of the slit width.

λ = 5 a

λ = a

λ = a/2

λ = a/3

λ = a/5

λ = a/10

KNIFE FIGHTS AND MISSILES
MATTHEW 6 26 Behold the fowls of the air: for they sow not, neither do they reap, nor gather into barns; yet your heavenly Father feedeth them. Are ye not much better than they? 34 Take therefore no thought for the morrow: for the morrow shall take thought for the things of itself. Sufficient unto the day is the evil thereof.

Why larger scale features in two-slit interference?

Resolving Power: Two Stars Seen Through a Slit

Rayleigh’s Criterion

Imaging a Star with a Telescope

Circular aperture resolution
In the printed figure, the lines are separated by 2 mm. Viewed at a distance, the two patterns look identical, but as you approach them, there is a point at which you can barely resolve the lines and tell the difference between the two images. From this distance L, you can calculate the angular resolution of your eyes: angular resolution = (2 mm)/L (in radians). Classroom demonstration: Hold up the figure and ask who can see the lines in one of the patterns. Usually no one beyond 4 meters will raise their hands. (This works best in a classroom which is 8 meters or more deep.) Using the above equation, L = 4 m corresponds to an angular resolution of 0.03 degrees. The diffraction limit of the eye can be calculated using Rayleigh's criterion: angular resolution = (1.22)(lambda)/D, where lambda is the wavelength of light (on the average, about 550 nm) and D is the diameter of the eye's pupil, which is about 5 mm indoors. This calculation results in an angular resolution of degrees. If your eyes could resolve images at the diffraction limit, you could resolve the lines in the printed pattern at a distance of 15 m!

What can a spy satellite resolve?
Low earth orbit: Too much drag below 300 km Delta IV max payload size ~5 m Very little light in x-ray, deep uv bands Strong atmospheric absorption below 300 nm. Fairly good transmission in visible band.

Cat’s eyes have pupils that can be modeled as vertical slits
Cat’s eyes have pupils that can be modeled as vertical slits. At night, would cats be more successful in resolving Two headlights on a distant car Vertically separated lights on the mast of a distant boat If the two sets of lights are the same distance away, the ability to resolve them would be the same.

Diffraction Gratings (Resolving power means something different here)
𝑅= 𝜆 Δ𝜆

Resolving Power of a Two Slit Pattern

Resolving Power with N Slits

Resolving Power of a Grating