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Chapter 33: Q. 1 (page 954)

FIGURE Q33.1 shows light waves passing through two closely spaced, narrow slits. The graph shows the intensity of light on a screen behind the slits. Reproduce these graph axes, including the zero and the tick marks locating the double-slit fringes, then draw a graph to show how the light-intensity pattern will appear if the right slit is blocked, allowing light to go through only the left slit. Explain your reasoning.

Short Answer

Expert verified

We'd get a single-slit pattern. The intensity in this pattern peaks below the slit and decreases as we move away from the centre. The central peak is twice as wide as the other peaks.

Step by step solution

01

Theory of light wave

The wave theory of light proposed by Christian Huygens has withstood the test of time and is now regarded as the foundation of optics. Let us now go over the wave theory of light in depth in this article. The Evolution of Light Wave Theory Light has always piqued the interest of philosophers and scientists.

02

Step2:Find light intensity

The light intensity will be similar to that of diffraction from a single thin slit. This assumes that the slit is no wider than 1 mm.

For the intensity versus position graph, we'd get something like this:

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Most popular questions from this chapter

In a double-slit interference experiment, which of the following actions (perhaps more than one) would cause the fringe spacing to increase? (a) Increasing the wavelength of the light. (b) Increasing the slit spacing. (c) Increasing the distance to the viewing screen. (d) Submerging the entire experiment in water.

For your science fair project you need to design a diffraction grating that will disperse the visible spectrum 400-700nmover30.0∘ in first order.
a How many lines per millimeter does your grating need?
bWhat is the first-order diffraction angle of light from a sodium lamp λ=589nm?

FIGURE shows two nearly overlapped intensity peaks of the sort you might produce with a diffraction grating . As a practical matter, two peaks can just barely be resolved if their spacing ∆yequals the width w of each peak, where wis measured at half of the peak’s height. Two peaks closer together than wwill merge into a single peak. We can use this idea to understand the resolution of a diffraction grating.

a. In the small-angle approximation, the position of the m=1peak of a diffraction grating falls at the same location as the m=1fringe of a double slit: y1=λL/d. Suppose two wavelengths differing by ∆lpass through a grating at the same time. Find an expression for localid="1649086237242" ∆y, the separation of their first-order peaks.

b. We noted that the widths of the bright fringes are proportional to localid="1649086301255" 1/N, where localid="1649086311478" Nis the number of slits in the grating. Let’s hypothesize that the fringe width is localid="1649086321711" w=y1/NShow that this is true for the double-slit pattern. We’ll then assume it to be true as localid="1649086339026" Nincreases.

c. Use your results from parts a and b together with the idea that localid="1649086329574" Δymin=wto find an expression for localid="1649086347645" Δλmin, the minimum wavelength separation (in first order) for which the diffraction fringes can barely be resolved.

d. Ordinary hydrogen atoms emit red light with a wavelength of localid="1649086355936" 656.45nm.In deuterium, which is a “heavy” isotope of hydrogen, the wavelength is localid="1649086363764" 656.27nm.What is the minimum number of slits in a diffraction grating that can barely resolve these two wavelengths in the first-order diffraction pattern?

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?

The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing. If the melanin lines on the wing are spaced 2.0μmapart, what is the first-order diffraction angle for green light λ=550nm?
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