The distance between the two slits is 0.0050 mm. Find the angles of the zeroth-, first-, second- and third-order bright fringes of interference produced by light with a wavelength of 550 nm.

Answers: 0°, 6.3°, 13°, 19°

When monochromatic light (light of a single wavelength) falls on two slits with a separation of 0.010 mm, the zeroth-order dark fringes are observed at a 2.0° angle. Find the wavelength.

Answer: 0.00070 mm or 7.0 10-7 m or 7.0 102 nm

A change in direction for waves when they encounter an obstacle or pass through an opening

Sound waves around a tree or through a doorHuygens’ principle states each point on a wave is a source for new waves.

Diffraction occurs to a greater extent if the wavelength and opening size are appropriate.

Openings much larger than the wavelength show very little diffraction.

Light waves through a door

Occurs because one part of the wave interferes with the other partsThe diagram shows 5 sample points, each producing waves.

The center line will be a point of constructive interference.Waves 1 and 5 travel the same distance to this line as do waves 2 and 4.

In order to reach a point above the center line, waves travel different distances.

Wave 3 travels 1/2 farther than wave 1, so destructive interference occurs.Similarly, wave 5 travels 1/2 farther than wave 3.

Thus, at the angle shown, destructive interference occurs and the screen is dark.

Suppose a laser shines on a screen. The round head of a pin (like those used to pin clothing) is placed between the laser and screen. You would expect to see a round shadow on the screen.

What will you see in the center of the shadow? Why?You will see a bright spot if you look very carefully. The waves diffract and all waves travel the same distance to the center of the shadow, creating constructive interference.

Many slits very closely spacedBehaves like the double slit, but maxima and minima are much brighter.

Monochromatic light produces bright and dark fringes.White light produces a full spectrum.

Similar to reflection off a CD surface

Diffraction gratings are used in spectrometers to separate light into its component colors.

Used to study the makeup of distant starsHelium’s spectrum was first observed on the sun, and helium was later discovered on Earth.

Click below to watch the Visual Concept.

Visual Concept

Equations are identical to those for two slit interference.

d is the distance between adjacent slits or lines.If there are 8000 lines per cm, then d = (1/8000) cm

If observing two distant objects, the diffraction patterns could overlap as shown.Without diffraction, there would be two bright spots on the screen.

The wavelength () and the opening size (D) determine the resolving power.

is the limiting angle between the two resolved objects measured in radians.Longer wavelengths require a larger aperture (D) to resolve distant objects. Because radio waves are long waves, radio telescopes are very large to accommodate the need for a large aperture.

= 1.22D

Imagine the opening is the pupil of your eye and the two sources are adjacent red and green pixels on your television screen.

What will you see?How would it change if your pupil opening was larger?How would it change if you were closer?How would it change if the pixels were farther apart?

A new astronomical facility is set for completion on Mount Wilson, in Georgia, by 1999. Named the Center for High Angular Resolution Astronomy (CHARA) Array, it comprises five telescopes whose individual images will be analyzed by computer. The resulting data will then be used to form a single high-resolution image of distant galaxies. The technique is similar to what is currently being done with radio telescopes. The CHARA Array will be used to observe radiation in the infrared portion of the spectrum with wavelengths as short as 2200 nm. Suppose 2200 nm light passes through a diffraction grating with 64 103 lines/m and produces a fringe at an angle of 34.0. What order maximum will the fringe be?

A new technology to improve the image quality of large-screen televisions has been developed recently. The entire screen would consist of tiny cells, each equipped with a movable mirror. The mirrors would change positions relative to the incoming signal, providing a brighter image. The entire screen would look like a diffraction grating with 250 000 lines/m. Imagine shining red light with a wavelength of 750 nm onto this grating. What order maximum would be observed at an angle of 48.6?