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Ch. 34 - The Wave Nature of Light: Interference and Polarization
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 34 - The Wave Nature of Light: Interference and PolarizationProblem 84
Chapter 33, Problem 84

Two narrow slits 0.070 mm apart are illuminated by a very bright 488-nm light source forming an interference pattern on a screen 4.0 m away. Calculate (a) the distance between the m = 0 and m = 1 lines in the pattern and (b) the distance between the m = 100 and m = 101 lines.

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Identify the given values: wavelength (λ) = 488 nm, distance between slits (d) = 0.070 mm, distance to screen (L) = 4.0 m. Convert all measurements to meters for consistency.
Use the formula for the position of the bright fringes in a double-slit interference pattern: y_m = (m * λ * L) / d, where m is the order of the fringe.
Calculate the position of the m = 0 fringe (central maximum) using the formula. Since m = 0, y_0 = 0.
Calculate the position of the m = 1 fringe using the formula. Substitute m = 1 into the formula to find y_1.
To find the distance between the m = 100 and m = 101 fringes, calculate the positions y_100 and y_101 using the same formula, and then find the difference between these two positions.

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Key Concepts

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

Young's Double Slit Experiment

This experiment demonstrates the wave nature of light through the interference pattern created when light passes through two closely spaced slits. The resulting pattern consists of bright and dark fringes due to constructive and destructive interference, respectively. The positions of these fringes can be calculated using the wavelength of the light and the distance between the slits.
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Young's Double Slit Experiment

Interference Pattern

An interference pattern is formed when two or more overlapping waves combine, resulting in regions of increased (constructive interference) and decreased (destructive interference) intensity. In the context of the double slit experiment, the pattern is characterized by alternating bright and dark lines on a screen, which can be quantified by the distance between specific order lines (m values).
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Path Difference

Path difference refers to the difference in distance traveled by two waves arriving at a point after passing through the slits. For constructive interference, this difference must be an integer multiple of the wavelength, while for destructive interference, it must be a half-integer multiple. The path difference is crucial for determining the positions of the interference fringes on the screen.
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Related Practice
Textbook Question

Consider two antennas radiating 6.8-MHz radio waves in phase with each other. They are located at points S₁ and S₂, separated by a distance d = 175 m, Fig. 34–50. Determine the points on the positive y-axis where the signals from the two sources will be out of phase (crests of one meet troughs of the other).

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Textbook Question

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of (a) 4, (b) 10, (c) 100?

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Textbook Question

A highly reflective mirror can be made for a particular wavelength at normal incidence by using two thin layers of transparent materials of indices of refraction n₁ and n₂ ( 1 < n₁ < n₂ ) on the surface of the glass (n > n₂). What should be the minimum thicknesses d₁ and d₂ in Fig. 34–49 in terms of the incident wavelength λ, to maximize reflection?

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Textbook Question

Suppose the mirrors in a Michelson interferometer are perfectly aligned and the path lengths to mirrors M₁ and M₂ are identical. With these initial conditions, an observer sees a bright maximum at the center of the viewing area. Now one of the mirrors is moved a distance x. Determine a formula for the intensity at the center of the viewing area as a function of x, the distance the movable mirror is moved from the initial position.

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Textbook Question

Two polarizers are oriented at 55° to each other and plane-polarized light is incident on them. If only 25% of the light gets through both of them, what was the initial polarization direction of the incident light?

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Textbook Question

Unpolarized light falls on two polarizer sheets whose axes are at right angles. (a) What fraction of the incident light intensity is transmitted? (b) What fraction is transmitted if a third polarizer is placed between the first two so that its axis makes a 58° angle with the axis of the first polarizer? (c) What if the third polarizer is in front of the other two?

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