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Chapter 33: Q. 27 (page 956)

You want to photograph a circular diffraction pattern whose central maximum has a diameter of 1.0cm. You have a helium neon laser (λ=633nm)and a0.12-mm-diameter pinhole. How far behind the pinhole should you place the screen that’s to be photographed?

Short Answer

Expert verified

Distance for the screen to be photographed, d=0.777m

Step by step solution

01

Aperture Diffraction

When light passes through a narrow opening, such as an aperture with a low f-number, it causes lens diffraction, which is an optical interference.

When the wavelength of light and the size of the opening are about the same, lens diffraction occurs.

02

Find the distance 

In the aperture diffraction experiment, the center width is given by,

w=2.44λLD

We can findLby solving parametrically.

L=wD2.44λ

03

Find the distance 

This will be the length in our situation.

L=wD2.44λ

localid="1650215739018" L=1×10-2m×1.2×10-4m2.44×6.33×10-7m

=0.777m

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Most popular questions from this chapter

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?

The pinhole camera of FIGURE images distant objects by allowing only a narrow bundle of light rays to pass through the hole and strike the film. If light consisted of particles, you could make the image sharper and sharper (at the expense of getting dimmer and dimmer) by making the aperture smaller and smaller. In practice, diffraction of light by the circular aperture limits the maximum sharpness that can be obtained. Consider two distant points of light, such as two distant streetlights. Each will produce a circular diffraction pattern on the film. The two images can just barely be resolved if the central maximum of one image falls on the first dark fringe of the other image. (This is called Rayleigh’s criterion, and we will explore its implication for optical instruments in Chapter 35.)

a. Optimum sharpness of one image occurs when the diameter of the central maximum equals the diameter of the pinhole. What is the optimum hole size for a pinhole camera in which the film is 20cmbehind the hole? Assume localid="1649089848422" λ=550nman average value for visible light.

b. For this hole size, what is the angle a (in degrees) between two distant sources that can barely be resolved?

c. What is the distance between two street lights localid="1649089839579" 1kmaway that can barely be resolved?

A 0.50-mm-wide slit is illuminated by light of wavelength 500nm. What is the width (inmm)of the central maximum on a screen2.0mbehind the slit?

Light from a helium-neon laser (λ=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?

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.
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