Chapter 28 Units of Chapter 28 - City University of New York

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Chapter 28

Physical Optics: Interference and Diffraction


Units of Chapter 28 •  Superposition and Interference

•  Young’s Two-Slit Experiment

•  Interference in Reflected Waves

•  Diffraction

•  Resolution

•  Diffraction Gratings


28-1 Superposition and Interference If two waves occupy the same space, their amplitudes add at each point. They may interfere either constructively or destructively.


28-1 Superposition and Interference

Interference is only noticeable if the light sources are monochromatic (so all the light has the same wavelength) and coherent (different sources maintain the same phase relationship over space and time).

Interference will be constructive where the two waves are in phase, and destructive where they are out of phase.


28-1 Superposition and Interference

In this illustration, interference will be constructive where the path lengths differ by an integral number of wavelengths,

and destructive where they differ by a half-odd integral number of wavelengths.


28-2 Young’s Two-Slit Experiment

In this experiment, the original light source need not be coherent; it becomes so after passing through the very narrow slits.

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28-2 Young’s Two-Slit Experiment

If light consists of particles, the final screen should show two thin stripes, one corresponding to each slit. However, if light is a wave, each slit serves as a new source of “wavelets,” as shown, and the final screen will show the effects of interference. This is called Huygens’s principle.


28-2 Young’s Two-Slit Experiment The path difference is given by:

Bright fringes:

Dark fringes:


Two slits separated by 0.050 mm located 1.50 m from a viewing screen are illuminated with monochromatic light. The third-order bright fringe is 5.30 cm from the zeroth-order bright fringe. Find (a) wavelength of the light and (b) separation between adjacent bright fringes.

Red light (wavelength 752 nm) passes through a pair of slits with a separation of 6.2×10-5 m. Find the angles corresponding to (a) the first bright fringe and (b) the second dark fringe above the central bright fringe.


28-3 Interference in Reflected Waves Reflected waves can interfere due to path length differences, but they can also interfere due to phase changes upon reflection.

There is no phase change when light reflects from a region with a lower index of refraction.

There is a half-wavelength phase change when light reflects from a region with a higher index of refraction, or from a solid surface.

There is also no phase change in the refracted wave.


28-3 Interference in Reflected Waves Constructive interference:

Destructive interference:

Example: An air wedge is formed between two glass plates separated at one edge by a very fine wire. When the wedge is illuminated from above by 600-nm light, 30 dark fringes are observed. Calculate the radius of the wire.


28-3 Interference in Reflected Waves

Interference can also occur when light refracts and reflects from both surfaces of a thin film. This accounts for the colors we see in oil slicks and soap bubbles.

Now, we have not only path differences and phase changes on reflection; we also must account for the change in wavelength as the light travels through the film.

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28-3 Interference in Reflected Waves Wavelength of light in a medium of index of refraction n:

Therefore, the condition for destructive interference, where t is the thickness of the film, is:

The condition for constructive interference:

The rainbow of colors we see is mainly due to the different thickness of the soap film.


28-3 Interference in Reflected Waves The phase changes upon reflection depend on the indices of refraction of the film and the surrounding media:

To see constructive interference:

If the total number of phase changes is even:

If the total number of phase changes is odd:


28-4 Diffraction •  Huygen’s principle requires that

the waves spread out after they pass through slits

•  This spreading out of light from its initial line of travel is called diffraction (when wave pass through small openings, around obstacles or by sharp edges)

Diffraction is why we can hear sound even though we are not in a straight line from the source – sound waves will diffract around doors, corners, and other barriers.

The amount of diffraction depends on the wavelength, which is why we can hear around corners but not see around them.

Single Slit Diffraction •  According to Huygen’s principle, each

portion of the slit acts as a source of waves •  The light from one portion of the slit can

interfere with light from another portion •  The resultant intensity on the screen

depends on the direction θ •  Destructive interference occurs for a single

slit of width W when:

Example: Laser light of 632.8 nm is directed through one slit or two slits and allowed to fall on a screen 2.60 m beyond. The figure shows the pattern on the screen with a centimeter ruler below it. Did the light pass through one slit or two slits? Find the width of the slit(s).

Diffraction Grating •  The condition for maxima is

d sin θbright = m λ •  If the incident radiation

contains several wavelengths, each wavelength deviates through a specific angle

•  Peaks are sharp

A grating spectroscope allows precise determination of wavelength.


28-6 Diffraction Gratings Diffraction can also be observed upon reflection from narrowly-spaced reflective grooves; the most familiar example is the recorded side of a CD. Some insect wings also display reflective diffraction, especially butterfly wings.

Example: A diffraction grating with 345 lines/mm is 1.00 m in front of a screen. What is the wavelength of light whose first-order maxima will be 16.4 cm from the central maximum on the screen?

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Summary of Chapter 28 •  When two waves are superposed, the result may be either constructive or destructive interference.

•  Monochromatic light consists of a single frequency.

•  Coherent light maintains a constant phase relationship.

•  Young’s two-slit experiment shows light and dark interference fringes.


Summary of Chapter 28

•  Bright fringes:

•  Dark fringes:

•  Thin films can form colors in reflected light through the destructive interference of other colors.


Summary of Chapter 28

•  When a wave encounters an obstacle or opening, it changes direction. This is called diffraction.

•  When monochromatic light passes through a narrow slit, a pattern of bright and dark fringes is produced.

•  Dark fringes (W is the width of the slit):

•  A diffraction grating is a large number of small slits. Principal maxima:

Chapter 28 Units of Chapter 28 - City University of New York

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