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Chapter 34: Problem 10

Huygens's Principle says that each point of a wave front in a slit is a point source of light emitting a spherical wavelet. A Huygens construction applies a) to any point anywhere in the path of the wave front. b) to any point in the path of the wave front where matter is present. c) only in slits.

Short Answer

Expert verified
Answer: A Huygens construction applies to any point anywhere in the path of the wave front.

Step by step solution

01

Understanding Huygens's Principle

Huygens's Principle states that at every point on a wave front, a secondary wavelet is emitted which then travels outward with the same velocity and frequency as the original wave. This principle can be applied to various types of waves, including light waves.
02

Huygens construction

Huygens construction is a geometric method to visualize the propagation of a wave front using Huygens's Principle. It can be used to predict the propagation of a wave in various scenarios, such as passing through a slit or a gap in the medium.
03

Analyzing the given statements

Now, we will analyze the given statements one by one: a) to any point anywhere in the path of the wave front: Huygens's Principle can be applied to any point on the wave front, and at that point, a secondary wavelet will be emitted. So, this statement seems to be correct. b) to any point in the path of the wave front where matter is present: Huygens's Principle can be applied to any point on the wave front, irrespective of the presence of matter. The presence of matter will only affect the way secondary wavelets are propagated. Thus, this statement is not accurate. c) only in slits: Although the idea of the Huygens's Principle is often associated with the wave propagation through slits, it is a general principle that can be applied in any scenario where wave propagation occurs. Thus, this statement is not accurate.
04

Conclusion

Based on our analysis of the statements: a) to any point anywhere in the path of the wave front. b) to any point in the path of the wave front where matter is present. c) only in slits. The correct answer is statement (a) - a Huygens construction applies to any point anywhere in the path of the wave front.

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Most popular questions from this chapter

Coherent monochromatic light with wavelength \(\lambda=514 \mathrm{nm}\) is incident on two thin slits that are separated by a distance \(d=0.500 \mathrm{~mm}\) The intensity of the radiation at a screen \(2.50 \mathrm{~m}\) away is \(180.0 \mathrm{~W} / \mathrm{cm}^{2}\). Determine the position \(v_{1}\) at which the intensity at the central peak (at \(y=0\) ) drops to \(I_{0} / 3\) (where \(I_{0}\) is the intensity at \(\theta=0^{\circ}\) ).

Coherent monochromatic light passes through parallel slits and then onto a screen that is at a distance \(L=2.40 \mathrm{~m}\) from the slits. The narrow slits are a distance \(d=2.00 \cdot 10^{-5} \mathrm{~m}\) apart. If the minimum spacing between bright spots is \(y=6.00 \mathrm{~cm},\) find the wavelength of the light.

A 5.000-cm-wide diffraction grating with 200 slits 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 \(\theta_{\mathrm{lb}}\) 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?

If Huygens's Principle holds everywhere, why does a laser beam not spread out? a) All the light waves that spread in the perpendicular direction from the beam interfere destructively. b) It does spread out, but the spread is so small that we don't notice it. c) Huygens's Principle isn't true in general; it only applies to slits, edges, and other obstacles. d) Lasers employ additional special beams to keep the main beam from spreading.

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 slits, what happens to the interference pattern? a) The pattern gets brighter. b) The pattern gets brighter, and the maxima are closer together. c) The pattern gets less bright, and the maxima are farther apart. d) There is no change in the pattern. e) The pattern becomes unfocused. f) The pattern disappears.
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