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Chapter 36: Q106P (page 1115)

Light of wavelength 500nm diffracts through a slit of width2μm 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 λ=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=mλDd .....(1)

Here,λ 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=3×500×10-9m×2m2×10-3m=0.0015m=1.5mm

Thus, the required distance is 1.5mm.

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Most popular questions from this chapter

If you look at something 40 m from you, what is the smallest length (perpendicular to your line of sight) that you can resolve, according to Rayleigh’s criterion? Assume the pupil of your eye has a diameter of 4.00 mm, and use 500 nm as the wavelength of the light reaching you.

A source containing a mixture of hydrogen and deuterium atoms emits red light at two wavelengths whose mean is 656.3 nm and whose separation is 0.180 nm. Find the minimum number of lines needed in a diffraction grating that can resolve these lines in the first order.

At night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings. The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer’s eye. (The central maxima of such patterns overlap the lamp.) (a) Would a particular ring become smaller or larger if the lamp were switched from blue to red light? (b) If a lamp emits white light, is blue or red on the outside edge of the ring?

Figure 36-46 is a graph of intensity versus angular positionfor the diffraction of an x-ray beam by a crystal. The horizontal scale is set byθs=2.00°.The beam consists of two wavelengths, and the spacing between the reflecting planes is0.94nm. What are the (a) shorter and (b) longer wavelengths in the beam?

For three experiments, Fig.36-31 gives the parameter of Eq. 36-20 versus angle in two-slit interference using light of wavelength 500 nm. The slit separations in the three experiments differ. Rank the experiments according to (a) the slit separations and (b) the total number of two slit interference maxima in the pattern, greatest first.
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