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Chapter 34: Problem 8

In Young's double-slit experiment, both slits were illuminated by a laser beam and the interference pattern was observed on a screen. If the viewing screen is moved farther from the slit, what happens to the interference pattern? a) The pattern gets brighter. b) The pattern gets brighter and closer together. c) The pattern gets less bright and farther apart. d) There is no change in the pattern. e) The pattern becomes unfocused. f) The pattern disappears.

Short Answer

Expert verified
Answer: c) The pattern gets less bright and farther apart.

Step by step solution

01

Review Young's Double-Slit Experiment Equations

Young's double-slit experiment demonstrates the wave nature of light, where the interference pattern on the screen is caused by the superposition of waves from two slits. The interference pattern on the screen features alternating bright and dark fringes. The relationship between the width of the fringes, the wavelength of the light, and the distance between the slits and the screen is given by the following formula: distance between fringes = \(\frac{wavelength \cdot screen\_distance}{distance\_between\_slits}\) We can use this formula to determine how the interference pattern changes when the screen distance is increased.
02

Evaluate the Effect of Increasing Screen Distance on the Interference Pattern

Let's analyze what happens to the interference pattern when we increase the screen distance. From the formula mentioned above, we can see that the distance between the fringes is directly proportional to the screen distance. So when the screen distance increases, the distance between the fringes should also increase.
03

Consider the Effect on Brightness

Now let's consider the brightness of the pattern. As the screen moves farther away from the slits, the total energy of the laser beam remains the same, but it is distributed over a larger area (due to the larger distance). As a result, the intensity (brightness) decreases as the area on which the energy is distributed increases. Hence, as the screen moves farther away from the slits, the pattern gets less bright.
04

Select the Appropriate Answer Choice

Using the information from Step 2 and Step 3, we can conclude that the interference pattern gets less bright and further apart when the screen is moved farther from the slits. Hence, the correct answer is: c) The pattern gets less bright and farther apart.

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Most popular questions from this chapter

A \(5.000-\mathrm{cm}\) -wide diffraction grating with 200 grooves is used to resolve two closely spaced lines (a doublet) in a spectrum. The doublet consists of two wavelengths, \(\lambda_{\mathrm{a}}=\) \(629.8 \mathrm{nm}\) and \(\lambda_{\mathrm{b}}=630.2 \mathrm{nm} .\) The light illuminates the entire grating at normal incidence. Calculate to four significant digits the angles \(\theta_{1 \mathrm{a}}\) and \(\theta_{1 \mathrm{~b}}\) with respect to the normal at which the first-order diffracted beams for the two wavelengths, \(\lambda_{\mathrm{a}}\) and \(\lambda_{\mathrm{b}}\), respectively, will be reflected from the grating. Note that this is not \(0^{\circ}\) What order of diffraction is required to resolve these two lines using this grating?

Many times, radio antennas occur in pairs. The effect is that they will then produce constructive interference in one direction while producing destructive interference in another direction - a directional antenna-so that their emissions don't overlap with nearby stations. How far apart at a minimum should a local radio station, operating at \(88.1 \mathrm{MHz},\) place its pair of antennae operating in phase such that no emission occurs along a line \(45.0^{\circ}\) from the line joining the antennae?

A Young's interference experiment is performed with monochromatic green light \((\lambda=540 \mathrm{nm}) .\) The separation between the slits is \(0.100 \mathrm{~mm},\) and the interference pattern on a screen shows the first side maximum \(5.40 \mathrm{~mm}\) from the center of the pattern. How far away from the slits is the screen?

What minimum path difference is needed to cause a phase shift by \(\pi / 4\) in light of wavelength \(700 . \mathrm{nm} \)

A Michelson interferometer is illuminated with a 600.-nm light source. How many fringes are observed if one of the mirrors of the interferometer is moved a distance of 200. \(\mu \mathrm{m} ?\)
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