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Chapter 36: Q106P (page 1115)

Light of wavelength 500nm diffracts through a slit of width2渭m and onto a screen that is 2maway. On the screen, what is the distance between the center of the diffraction pattern and the third diffraction minimum?

Short Answer

Expert verified

The distance between the center of the diffraction pattern and the third diffraction minimum is1.5mm .

Step by step solution

01

Given data:

The wavelength of incident light 位=500nm:

Slit width: d=2mm

Distance of screen from slit: D=2m

02

Diffraction from a single slit:

The distance of the mth order single slit diffraction minima from thecentral maxima for slit width d and screen distance D is

x=m位Dd .....(1)

Here,位 is the wavelength of the incident light.

03

Determining the distance of the third minimal from central maxima

Calculate the distance of the third minima from the central maxima by substituting known values into equation (1).

x=3脳500脳10-9m脳2m2脳10-3m=0.0015m=1.5mm

Thus, the required distance is 1.5mm.

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Most popular questions from this chapter

An astronaut in a space shuttle claims she can just barely resolve two point sources on Earth鈥檚 surface, 160 km below. Calculate their (a) angular and (b) linear separation, assuming ideal conditions. Take 位 = 540 nm and the pupil diameter of the astronaut鈥檚 eye to be 5.0 mm.

Light of frequency f illuminating a long narrow slit produces a diffraction pattern. (a) If we switch to light of frequency 1.3f, does the pattern expand away from the center or contract toward the center? (b) Does the pattern expand or contract if, instead, we submerge the equipment in clear corn syrup?

For the situation in Questions 9 and Fig. 1, if instead we increased the grating spacing, would (a) the half-widths of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place?

Floaters. The floaters you see when viewing a bright, featureless background are diffraction patterns of defects in the vitreous humor that fills most of your eye. Sighting through a pinhole sharpens the diffraction pattern. If you also view a small circular dot, you can approximate the defect鈥檚 size. Assume that the defect diffracts light as a circular aperture does. Adjust the dot鈥檚 distance L from your eye (or eye lens) until the dot and the circle of the first minimum in the diffraction pattern appear to have the same size in your view. That is, until they have the same diameter D'on the retina at distance L'=2cmfrom the front of the eye, as suggested in Fig. 36-42a, where the angles on the two sides of the eye lens are equal. Assume that the wavelength of visible light is 位=550nm. If the dot has diameter D=2.0mmand is distance L=45.0cmfrom the eye and the defect is x=6.0mm in front of the retina (Fig. 36-42b), what is the diameter of the defect?

(a) For a given diffraction grating, does the smallest difference 螖位in two wavelengths that can be resolved increase, decrease, or remain the same as the wavelength increases? (b) For a given wavelength region (say, around 500 nm), is 螖位 greater in the first order or in the third order?
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