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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 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 double-slit experiment is set up using a helium-neon laser (λ=633nm). Then a very thin piece of glass (n=1.50) is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the m=10 dark fringe. How thick is the glass?

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.

Your artist friend is designing an exhibit inspired by circular-aperture diffraction. A pinhole in a red zone is going to be illuminated with a red laser beam of wavelength 670nm, while a pinhole in a violet zone is going to be illuminated with a violet laser beam of wavelength 410nm. She wants all the diffraction patterns seen on a distant screen to have the same size. For this to work, what must be the ratio of the red pinhole’s diameter to that of the violet pinhole?

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 5.0×10-16sin 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 Δϕ0between 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?

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