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Chapter 33: Q. 13 (page 955)

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656nm (red) and 486nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 500lines/mm, and the light is observed on a screen 1.50m behind the grating. What is the distance between the first-order red and blue fringes?

Short Answer

Expert verified

The distance between red and blue fringes is14.5cm.

Step by step solution

01

Formula for distance

The center of them-th fringe is given by,

Ym=尝迟补苍胃m

=Ltansin-1尘位d

localid="1649218383524" dis the distance between gratings

localid="1649218434130" 位is wavelength

localid="1649218442071" 胃mis diffraction angle

02

Calculation for distance

The grating constant is500lines/mm.

There will be a space between two succeeding gratings.

d=1脳10-3500

=2脳10-6m炉

So,

螖驰=尝迟补苍胃1,red-尝迟补苍胃1,blue

=Ltansin-1位redd-tansin-1位blued

In terms of numbers,

螖驰=1.5tansin-10.6562-tansin-10.4862

=14.5cm

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Most popular questions from this chapter

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 4.0-cm-wide diffraction grating has 2000 slits. It is illuminated by light of wavelength 550nm. What are the angles (in degrees) of the first two diffraction orders?

FIGURE Q33.1 shows light waves passing through two closely spaced, narrow slits. The graph shows the intensity of light on a screen behind the slits. Reproduce these graph axes, including the zero and the tick marks locating the double-slit fringes, then draw a graph to show how the light-intensity pattern will appear if the right slit is blocked, allowing light to go through only the left slit. Explain your reasoning.

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.

FIGURE P33.56 shows the light intensity on a screen behind a single slit. The slit width is 0.20mmand the screen is 1.5mbehind the slit. What is the wavelength (in nm) of the light?

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