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Chapter 33: Q.65 (page 958)

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.

Short Answer

Expert verified

The minimum diameter of the circular opening from which the laser beam emerges0.50m

Step by step solution

01

Maximum Diameter

We should compute cartesian coordinates and for size of the light's "bullet" by using equations for the length of the main maximum:

w=2.44位LD鈬�D=2.44位Lw

localid="1650221494106" D=2.44脳5.32脳10鈭�7m脳3.84脳108m1脳103m=0.499m(Numerically)

02

Minimum Diameter

Lets remember and we want is to round right, still not down due, is because we're seeking for shortest length which might help to attain this. As a findings, we just round the result to D=0.50m.

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Most popular questions from this chapter

FIGURE shows the light intensity on a viewing screen behind a circular aperture. What happens to the width of the central maximum if

a. The wavelength of the light is increased?

b. The diameter of the aperture is increased?

c. How will the screen appear if the aperture diameter is less than the light wavelength?

Light from a helium-neon laser (位=633nm)passes through a circular aperture and is observed on a screen 4.0mbehind the aperture. The width of the central maximum is2.5cm. What is the diameter (in mm) of the hole?

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.

Light of wavelength 600nmpasses though two slits separated by 0.20mmand is observed on a screen 1.0mbehind the slits. The location of the central maximum is marked on the screen and labeled y=0.

a. At what distance, on either side of y=0, are the m=1bright fringes?

b. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0脳10-16sin comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay?

c. With the glass in place, what is the phase difference 螖蠒0between the two waves as they leave the slits?2

d. The glass causes the interference fringe pattern on the screen to shift sideways. Which way does the central maximum move (toward or away from the slit with the glass) and by how far?

A diffraction grating with 600linesmmis illuminated with light of wavelength 510nm. A very wide viewing screen is2.0m behind the grating.
aWhat is the distance between the twom=1 bright fringes?
bHow many bright fringes can be seen on the screen?
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