Ch 33: Wave Optics

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 33: Wave Optics

Problem 39a

Chapter 33, Problem 39a

FIGURE P33.39 shows the light intensity on a screen 2.5 m behind an aperture. The aperture is illuminated with light of wavelength 620 nm. Is the aperture a single slit or a double slit? Explain.

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Examine the intensity pattern shown in the graph. The graph displays a series of evenly spaced peaks and troughs, which is characteristic of an interference pattern.

Understand the difference between single-slit and double-slit diffraction patterns. A single-slit pattern typically has a central bright fringe that is much wider than the other fringes, with intensity decreasing for higher-order fringes. A double-slit pattern, on the other hand, shows evenly spaced bright and dark fringes of similar width.

Note that the graph provided shows evenly spaced peaks of similar width and intensity, which is indicative of a double-slit interference pattern rather than a single-slit diffraction pattern.

Consider the wavelength of the light (620 nm) and the distance to the screen (2.5 m). These parameters are consistent with the formation of a double-slit interference pattern, as the spacing between the fringes depends on the wavelength and the geometry of the setup.

Conclude that the aperture is a double slit based on the observed pattern and the characteristics of interference phenomena.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Diffraction

Diffraction is the bending of waves around obstacles and the spreading of waves when they pass through narrow openings. It is a fundamental phenomenon observed in wave behavior, particularly with light. The extent of diffraction depends on the wavelength of the light and the size of the aperture. In the context of the question, diffraction patterns can indicate whether the aperture is a single slit or a double slit based on the resulting intensity distribution.

Interference Patterns

Interference patterns arise when two or more waves overlap and combine, leading to regions of constructive and destructive interference. In the case of light passing through slits, these patterns manifest as alternating bright and dark fringes on a screen. A double slit typically produces a more complex interference pattern with multiple bright and dark bands, while a single slit results in a simpler pattern. Analyzing the intensity graph can help determine the type of aperture based on the pattern observed.

Wavelength

Wavelength is the distance between successive peaks of a wave and is a critical factor in wave behavior, including diffraction and interference. The wavelength of light affects how it interacts with apertures and obstacles, influencing the resulting patterns. In this question, the given wavelength of 620 nm (nanometers) is essential for calculating the expected diffraction and interference effects, which can help distinguish between a single slit and a double slit based on the observed intensity distribution.

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Textbook Question

Light from a helium-neon laser (λ = 633 nm) passes through a circular aperture and is observed on a screen 4.0 m behind the aperture. The width of the central maximum is 2.5 cm. What is the diameter (in mm) of the hole?

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Textbook Question

Two vertical, high-frequency radio antennas are 20 m apart. 2.0 km away, in a plane parallel to the plane of the antennas, 'bright' spots of radio intensity are spaced 5.0 m apart, separated by spots with almost no radio intensity. What is the radio frequency?

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Textbook Question

You want to photograph a circular diffraction pattern whose central maximum has a diameter of 1.0 cm. You have a helium-neon laser (λ=633 nm) and a 0.12-mm-diameter pinhole. How far behind the pinhole should you place the screen that's to be photographed?

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Textbook Question

FIGURE P33.40 shows the light intensity on a screen 2.5 m behind an aperture. The aperture is illuminated with light of wavelength 620 nm. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing between the slits?

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Textbook Question

Helium atoms emit light at several wavelengths. Light from a helium lamp illuminates a diffraction grating and is observed on a screen 50.00 cm behind the grating. The emission at wavelength 501.5 nm creates a first-order bright fringe 21.90 cm from the central maximum. What is the wavelength of the bright fringe that is 31.60 cm from the central maximum?

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Textbook Question

A Michelson interferometer uses red light with a wavelength of 656.45 nm from a hydrogen discharge lamp. How many bright-dark-bright fringe shifts are observed if mirror M₂ is moved exactly 1 cm?

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