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Chapter 33: Q. 10 (page 954)

A Michelson interferometer is set up to display constructive interference (a bright central spot in the fringe pattern of Figure) using light of wavelength l. If the wavelength is changed to 位/2, does the central spot remain bright, does the central spot become dark, or do the fringes disappear? Explain. Assume the fringes are viewed by a detector sensitive to both wavelengths.

Short Answer

Expert verified

The brightness of the central maxima will be maintained.

Step by step solution

01

Introduction

Fringe is the alternately light and dark band that forms as a result of interference. When two light waves collide, destructive and constructive interference is created. Constructive interference causes the brilliant band, while interference causes the dark band.

02

Explanation

Because there is no phase difference at the central spot, even if the wavelength is hung, the central maxima will stay unaltered. When estimating the intensity of the centre maxima, the wavelength variation is not regarded in any way.

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Most popular questions from this chapter

3. FIGURE Q33.3 shows the viewing screen in a double-slit experiment. FringeCis the central maximum. What will happen to the fringe spacing if

a. The wavelength of the light is decreased?

b. The spacing between the slits is decreased?

c. The distance to the screen is decreased?

d. Suppose the wavelength of the light islocalid="1649170567955" 500nm. How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0kmin diameter. Staying within this diameter is accomplished by using a special large diameter laser. If 位=532nm, what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is384,000km.

To illustrate one of the ideas of holography in a simple way, consider a diffraction grating with slit spacing d. The small-angle approximation is usually not valid for diffraction gratings, because dis only slightly larger than 位, but assume that the 位/dratio of this grating is small enough to make the small-angle approximation valid.

a. Use the small-angle approximation to find an expression for the fringe spacing on a screen at distance Lbehind the grating.

b. Rather than a screen, suppose you place a piece of film at distance L behind the grating. The bright fringes will expose the film, but the dark spaces in between will leave the film unexposed. After being developed, the film will be a series of alternating light and dark stripes. What if you were to now 鈥減lay鈥� the film by using it as a diffraction grating? In other words, what happens if you shine the same laser through the film and look at the film鈥檚 diffraction pattern on a screen at the same distance L? Demonstrate that the film鈥檚 diffraction pattern is a reproduction of the original diffraction grating

A 500line/mmdiffraction grating is illuminated by light of wavelength 510nm.How many bright fringes are seen on a 2.0-m-wide screen located 2.0mbehind the grating?

You've found an unlabeled diffraction grating. Before you can use it, you need to know how many lines per it has. To find out, you illuminate the grating with light of several different wavelengths and then measure the distance between the two first-order bright fringes on a viewing screen 150cmbehind the grating. Your data are as follows:


Use the best-fit line of an appropriate graph to determine the number of lines per mm.
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