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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?

An instructor uses light of wavelength \(633 \mathrm{nm}\) to create a diffraction pattern with a slit of width \(0.135 \mathrm{~mm} .\) How far away from the slit must the instructor place the screen in order for the full width of the central maximum to be \(5.00 \mathrm{~cm} ?\)

White light shines on a sheet of mica that has a uniform thickness of \(1.30 \mu \mathrm{m} .\) When the reflected light is viewed using a spectrometer, it is noted that light with wavelengths of \(433.3 \mathrm{nm}, 487.5 \mathrm{nm}, 557.1 \mathrm{nm}, 650.0 \mathrm{nm}\), and \(780.0 \mathrm{nm}\) is not present in the reflected light. What is the index of refraction of the mica?

A Newton's ring apparatus consists of a convex lens with a large radius of curvature \(R\) placed on a flat glass disc. (a) Show that the distance \(x\) from the center to the air, thickness \(d,\) and the radius of curvature \(R\) are given by \(x^{2}=2 R d\) (b) Show that the radius of nth constructive interference is given by \(x_{\mathrm{n}}=\left[\left(n+\frac{1}{2}\right) \lambda R\right]^{1 / 2} .\) (c) How many bright fringes may be seen if it is viewed by red light of wavelength 700\. \(\mathrm{nm}\) for \(R=10.0 \mathrm{~m},\) and the plane glass disc diameter is \(5.00 \mathrm{~cm} ?\)

Plane light waves are incident on a single slit of width \(2.00 \mathrm{~cm} .\) The second dark fringe is observed at \(43.0^{\circ}\) from the central axis. What is the wavelength of the light?
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