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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 λ=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=2.44λLD⇒D=2.44λLw

localid="1650221494106" D=2.44×5.32×10−7m×3.84×108m1×103m=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

A double-slit experiment is performed with light of wavelength630nm. The bright interference fringes are spaced 1.8mm apart on the viewing screen. What will the fringe spacing be if the light is changed to a wavelength of 420nm ?

A student performing a double-slit experiment is using a green laser with a wavelength of 530nm.. She is confused when the m=5maximum does not appear. She had predicted that this bright fringe would be 1.6cmfrom the central maximum on a screen 1.5mbehind the slits.

a. Explain what prevented the fifth maximum from being observed.

b. What is the width of her slits?

For what slit-width-to-wavelength ratio does the first minimum of a single-slit diffraction pattern appear at (a) 30°, (b) 60°, and (c) 90°?

Narrow, bright fringes are observed on a screen behind a diffraction grating. The entire experiment is then immersed in water. Do the fringes on the screen get closer together, get farther apart, remain the same, or disappear? Explain.

Light of wavelength550nm illuminates a double slit, and the interference pattern is observed on a screen. At the position of the m=2 bright fringe, how much farther is it to the more distant slit than to the nearer slit?
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