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Chapter 33: Q.28 (page 956)

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鈥檚 diameter to that of the violet pinhole?

Short Answer

Expert verified

Ratio of red pinhole diameter to violet pinhole ,DredDviolet=1.63

Step by step solution

01

Laser Beam

A laser beam is a single-wavelength stream of concentrated, coherent light.

02

Find ratio

In order for the diffraction patterns from the two pinholes to have the same size, the angle of the first minimum in the two patterns must be the same, where this angle is given by the following relation

胃1=1.22位D

When you multiply 胃1by the number of pinholes, you get

1.22位redDred=1.22位violetDviolet

rearranging the equations,

DredDviolet=位red位violet=670nm410nm=1.63

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Most popular questions from this chapter

A diffraction grating with 600linesmmis illuminated with light of wavelength 510nm. A very wide viewing screen is2.0m behind the grating.
aWhat is the distance between the twom=1 bright fringes?
bHow many bright fringes can be seen on the screen?

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.

One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you're not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 1cmacross, and you estimate that the distance from the window shade to the wall is about 3m.. Estimate (a) the average wavelength of the sunlight (in nm ) and (b) the diameter of the pinhole (in mm ).

Two 50-渭m-wide slits spaced 0.25mmapart are illuminated by blue laser light with a wavelength of 450nm. The interference pattern is observed on a screen2.0m behind the slits. How many bright fringes are seen in the central maximum that spans the distance between the first missing order on one side and the first missing order on the other side?

FIGURE shows the light intensity on a viewing screen behind a single slit of width a. The light鈥檚 wavelength is 位. Is 位<a,位=a, 位>a, oris it not possible to tell? Explain.
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