Like other waves, light waves can add constructively and destructively as shown above. Examples: –Colors seen in soap bubbles –Colors seen in a thin film of oil on water Click to add text

Waves must maintain a constant phase relationship, or be coherent. –In figure a, the waves are in phase. –In figure b, the waves are out of phase. Incoherent light has phase relationships that shift. –Interference will not be observed.

Waves must maintain a constant phase relationship, or be coherent. –In figure a, the waves are in phase. –In figure b, the waves are out of phase. Incoherent light has phase relationships that shift. –Interference will not be observed.

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Light from a single source passes through two slits, creating two coherent sources. The two waves then spread out in all directions (Huygen’s Principle) and interfere with each other. –Constructive interference creates bright spots on a screen. –Destructive interference creates dark spots on a screen.

The two waves travel the same distance to the center of the screen. –They arrive in phase. –Constructive interference occurs. –A bright spot is seen in the middle of the screen.

The top wave travels a distance of 1 farther than the bottom wave. –They arrive at the screen in phase. –Constructive interference occurs. –A bright spot is seen. What distances other than 1 would result in a bright spot on the screen?

The top wave travels a distance of (1/2) farther than the bottom wave. –They arrive at the screen out of phase. –Destructive interference occurs. –A dark area is seen. What distances other than (1/2) would result in a dark area on the screen?

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Because the screen is distant, l 1 and l 2 are nearly parallel. This makes the angles almost equal. –d sin  is the extra distance the lower wave travels while moving to a common point on the screen.

For constructive interference, d sin  (path length difference) is a whole number of wavelengths. For destructive interference, the path length difference is an odd number of half-wavelengths (1/2, 3/2, 5/2 and so on).

Comet Hale-Bopp, which came close to Earth in 1997, has a complex chemical composition. To understand it, scientists analyzed radiation emitted from the radiation with a wavelength of nm. Using a double-slit apparatus with a slit separation of 1.20  10 3 nm to measure these wavelengths, at what angle would a fifth- order maximum be observed?

A typical optic fiber has a thickness of only 6.00  10 3 nm. Consider a beam from a standard He-Ne laser that has a wavelength equal to 633 nm. Suppose this beam is incident upon two parallel slits that are separated by a distance equal to the width of a typical optic fiber. What is the angle at which the first dark fringe would be observed?

The smallest printed and bound book, which contains the children’s story “Old King Cole,” was published in The book’s width is about 0.80 mm. Imagine a double-slit apparatus with a separation equal to the width of this book. What wavelength would produce a third-order minimum at an angle of 1.6  ?

The water in Earth’s atmosphere blocks most of the infrared waves coming from space. In order to observe light of this wavelength, the Kuiper Airborne Observatory has been developed. The observatory consists of an optical telescope mounted inside a modified C-141 aircraft. The plane flies at altitudes where the relative humidity is very low and where the incoming infrared radiation has not yet been significantly absorbed. Suppose a double-slit arrangement with a 15.0  m slit separation is used to analyze infrared waves received by the telescope and that a second-order maximum is observed at 19.5 . Determine the wave’s wavelength.