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Chapter 33: Q. 32 (page 956)

A Michelson interferometer uses light from a sodium lamp. Sodium atoms emit light having wavelengths 589.0nmand 589.6nm. The interferometer is initially set up with both arms of equal length L1=L2, producing a bright spot at the center of the interference pattern. How far must mirrorM2be moved so that one wavelength has produced one more new maximum than the other wavelength?

Short Answer

Expert verified

Length from one more new maximum than other wavelength, L=0.2894mm

Step by step solution

01

Sodium Lamp

These lamps are mostly utilized for street and industrial lighting.

The lamp works by using vaporized sodium metal to create an electric arc.

To help begin the lamp or adjust its hue, other compounds and gases are utilized.

02

find the formula for length

For the sake of clarity, we will refer to the distance travelled by Lrather than 螖L.

The gap between both the number of fringes produced by each wavelength will be determined by

localid="1650215416013" 螖m=2L位2-2L位1

=2L位1-位2位1位2

We can find it by solving for the distance para metrically.

L=螖m脳位1位22螖位

03

Substitute values to find length

In our scenario, we will have the following numbers:

L=螖m脳位1位22螖位

L=1脳5.890脳10-7m脳5.896脳10-7m2脳(5.896-5.890)脳10-7m=2.894脳10-4m

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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?

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?

The intensity at the central maximum of a double-slit interference pattern is 4I1. The intensity at the first minimum is zero. At what fraction of the distance from the central maximum to the first minimum is the intensity I1? Assume an ideal double slit.

A triple-slit experiment consists of three narrow slits, equally spaced by distance dand illuminated by light of wavelength 位. Each slit alone produces intensity I1on the viewing screen at distanceL.
aConsider a point on the distant viewing screen such that the path-length difference between any two adjacent slits is位. What is the intensity at this point?
bWhat is the intensity at a point where the path-length difference between any two adjacent slits is位2?

aFind an expression for the positions y1of the first-order fringes of a diffraction grating if the line spacing is large enough for the small-angle approximation tan鈦�胃鈮�sin鈦�胃鈮�胃to be valid. Your expression should be in terms of d,Land位.
b. Use your expression from part a to find an expression for the separation鈭�yon the screen of two fringes that differ in wavelength by鈭�位.
cRather than a viewing screen, modern spectrometers use detectors-similar to the one in your digital camera-that are divided into pixels. Consider a spectrometer with a 333lines/mmgrating and a detector with 100pixels/mmlocated 12cmbehind the grating. The resolution of a spectrometer is the smallest wavelength separation 鈭�位minthat can be measured reliably. What is the resolution of this spectrometer for wavelengths near localid="1649156925210" 550nm, in the center of the visible spectrum? You can assume that the fringe due to one specific wavelength is narrow enough to illuminate only one column of pixels.
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