MSTC Physics C Chapter 24 Section 3

Diffraction Spreading of waves into a region behind an obstruction Occurs when waves pass through small openings, around obstacles, or by sharp edges

Diffraction Longer the wavelength, compared to the width of the opening, the greater the diffraction

Diffraction Resemble interference patterns because they result from constructive and destructive interference

Diffraction According to Huygen’s principle, each portion of a slit acts as a source of waves Hence, one portion of a slit can interfere with light from another portion Suppose slit is composed of 5 particles Point 1 travels the shortest distance Point 5 travels the farthest The first dark fringe occurs when the extra distance traveled by the wave from source 3 is 1/2λ longer The waves from 1 and 3 are opposite and destructive interfere At this angle each wave from the upper half cancels a wave from the bottom half that travels 1/2λ farther For other angles some of the light remains uncanceled and the screen appears bright

Diffraction According to Huygen’s principle, each portion of a slit acts as a source of waves Hence, one portion of a slit can interfere with light from another portion Suppose slit is composed of 5 particles Point 1 travels the shortest distance Point 5 travels the farthest The first dark fringe occurs when the extra distance traveled by the wave from source 3 is 1/2λ longer The waves from 1 and 3 are opposite and destructive interfere At this angle each wave from the upper half cancels a wave from the bottom half that travels 1/2λ farther For other angles some of the light remains uncanceled and the screen appears bright

Diffraction For destructive interference, w sinΘ = m λ m=1,2,3,….. where w=width of slit and Θ=angle of particular minimum

Sample problem Light of wavelength 580 nm is incident on a slit of width 0.3 mm. The observing screen is placed 2 m from the slit. Find the positions of the first dark fringes and the width of the central bright fringe. What is the width of the first order bright fringe?

Single Slit diffraction Top photo is with monochromatic light. Bottom photo is with white light. Note: brightest and widest in the middle

Single slit diffraction As slit width decreases, note that the width of the central max also increases

Double slit interference Top picture is monochromatic light Bottom picture is white light Note: intensity stays pretty consistent Note that all bands are equal in width and the brightness stays fairly constant

Diffraction grating Consists of a large number of equally spaced parallel slits Can be made by engraving parallel lines on a glass plate with a precision machining technique Typical grating consists of several thousand lines per centimeter ex – 5000 lines/cm d ( distance between slits) = 1/5000 cm = 2 x 10-4 cm

Diffraction grating Each slit acts as a source of waves where all waves start at the slits in phase

Diffraction grating Each slit produces diffraction

Diffraction grating The diffracted beams interfere with each other to produce the final pattern

Diffraction grating There will be some arbitrary direction Θ measured from the horizontal where the waves must travel different paths lengths before reaching the screen

Diffraction grating If the path length difference is some multiple of a wavelength all waves are in phase and constructive interference Intensity drops off gradually as work out from center

Diffraction grating Constructive interference dsinΘ = mλ where m = 0,1,2,3,…

Sample Problem Monochromatic light from a helium neon laser (632.8 nm) is incident normally on a diffraction grating containing 6000 lines/cm. Find the angles at which one would observe the first order maximum, second order maximum, and so forth.