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Chapter 33: Q. 57 (page 957)

FIGURE P33.56 shows the light intensity on a screen behind a single slit. The wavelength of the light is 600nmand the slit width is 0.15mm. What is the distance from the slit to the screen?

Short Answer

Expert verified

The distance from the slit to the screen1.25m

Step by step solution

01

Central Cringe

Remember that the entire width of a main fringes in the single study is given by

wc=2λLa

In an intellectual result, we can resolve parametrically only for the length to find a solution.

L=awc2λ

02

Length

In terms of quantity, our length will just be

L=1.5×10−4⋅1×10−22⋅6×10−7=1.25m

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Most popular questions from this chapter

a. Green light shines through a 100-mm-diameter hole and is observed on a screen. If the hole diameter is increased by 20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.

b. Green light shines through a 100−μm-diameter hole and is observed on a screen. If the hole diameter is increased by20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.

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 helium-neon laser (λ=633nm) illuminates a diffraction grating. The distance between the two m=1 bright fringes is 32cm on a screen 2.0m behind the grating. What is the spacing between slits of the grating?

a. Green light will shine through a hole with a 100-mm-diameter hole of and is seen on a screen. Does the circular point of lights 20%,is on the screen shrink in diameter, rise in diameter, or remain the same in diameter by? Explain.

b. Green light will shine through a hole with a 100-μmdiameter of and is seen on a screen. Does the circular point of lights is 20%,on the screen shrink in diameter, rise in diameter, or remain the same in diameter by? Explain.

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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