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Chapter 33: Q. 21 (page 955)

Light from a helium-neon laser (λ=633nm) is incident on a single slit. What is the largest slit width for which there are no minima in the diffraction pattern?

Short Answer

Expert verified

The largest width fora<633nmin the diffraction pattern

Step by step solution

01

Helium-neon laser

Helium-neon (He-Ne) lasers are often used for interferometry because they are inexpensive and produce a consistent, visible output. They operate at a wavelength of 633nmby default, although customized versions with outputs at various visible and infrared wavelengths are also available.

02

Step2: 

The angles within which dark fringes are detected in a single-slit experiment are given by

sinθp=pλa

where a is the slit width and p is the order To avoid dark fringes on the screen, the sine must be higher than 1, which means that

λa>1

Rearrange this,

a<λ

By this,

a<6.33·10-7m

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Most popular questions from this chapter

A 600 line/mm diffraction grating is in an empty aquarium tank. The index of refraction of the glass walls is nglass=1.50. A helium-neon laser (λ=633nm)is outside the aquarium. The laser beam passes through the glass wall and illuminates the diffraction grating.

a. What is the first-order diffraction angle of the laser beam?

b. What is the first-order diffraction angle of the laser beam after the aquarium is filled with water nwater=1.33?

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?

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?

Scientists shine a laser beam on a 35-μm-wide slit and produce a diffraction pattern on a screen 70cmbehind the slit. Careful measurements show that the intensity first falls to 25%of maximum at a distance of7.2mmfrom the center of the diffraction pattern. What is the wavelength of the laser light?

Hint: Use the trial-and-error technique demonstrated in Example 33.5to solve the transcendental equation.

Light of 630nmwavelength illuminates two slits that are0.25mmapart. FIGURE EX33.5shows the intensity pattern seen on a screen behind the slits. What is the distance to the screen?
See all solutions

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