Problem 3: Anti-reflective coatings on lenses use thin-film interference to eliminate the reflection of a particular color. Suppose a glass lens (ng= 1.58) is covered with a thin film (n= 1.34) to prevent green light (2 = 538 nm) from being reflected. Part (a) Write an expression for the minimum thickness the film can have, t.

Problem 3: Anti-reflective coatings on lenses use thin-film interference to eliminate the reflection of a particular color. Suppose a glass lens (ng= 1.58) is covered with a thin film (n= 1.34) to prevent green light (2 = 538 nm) from being reflected. Part (a) Write an expression for the minimum thickness the film can have, t.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter27: Wave Optics

Section: Chapter Questions

Problem 71P: Figure CQ27.4 shows an unbroken soap film in a circular frame. The film thickness increases from top...

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In Figure P36.10 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4? Figure P36.10
Interference fringes are produced using Lloyds mirror and a source S of wavelength = 606 nm as shown in Figure P36.41. Fringes separated by y = 1.20 mm are formed on a screen a distance L = 2.00 m from the source. Find the vertical distance h of the source above the reflecting surface. Figure P36.41
A Fraunhofer diffraction pattern is produced on a screen located 1.00 m from a single slit. If a light source of wavelength 5.00 107 m is used and the distance from the center of the central bright fringe to the first dark fringe is 5.00 103 m, what is the slit width? (a) 0.010 0 mm (b) 0.100 mm (c) 0.200 mm (d) 1.00 mm (e) 0.005 00 mm
Two slits are separated by 0.320 mm. A beam of 500-nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range 30.0 30.0.
Show that the distribution of intensity in a double-slit pattern is given by Equation 36.9. Begin by assuming that the total magnitude of the electric field at point P on the screen in Figure 36.4 is the superposition of two waves, with electric field magnitudes E1=E0sintE2=E0sin(t+) The phase angle in in E2 is due to the extra path length traveled by the lower beam in Figure 36.4. Recall from Equation 33.27 that the intensity of light is proportional to the square of the amplitude of the electric field. In addition, the apparent intensity of the pattern is the time-averaged intensity of the electromagnetic wave. You will need to evaluate the integral of the square of the sine function over one period. Refer to Figure 32.5 for an easy way to perform this evaluation. You will also need the trigonometric identity sinA+sinB=2sin(A+B2)cos(AB2)
Both sides of a uniform film that has index of refraction n and thickness d are in contact with air. For normal incidence of light, an intensity minimum is observed in the reflected light at λ2 and an intensity maximum is observed at λ1, where λ1 > λ2. (a) Assuming no intensity minima are observed between λ1 and λ2, find an expression for the integer m in Equations 27.13 and 27.14 in terms of the wavelengths λ1 and λ2. (b) Assuming n = 1.40, λ1 = 500 nm, and λ2 = 370 nm, determine the best estimate for the thickness of the film.
Table P35.80 presents data gathered by students performing a double-slit experiment. The distance between the slits is 0.0700 mm, and the distance to the screen is 2.50 m. The intensity of the central maximum is 6.50 106 W/m2. What is the intensity at y = 0.500 cm? TABLE P35.80
Figure CQ27.4 shows an unbroken soap film in a circular frame. The film thickness increases from top to bottom, slowly at first and then rapidly. As a simpler model, consider a soap film (n = 1.33) contained within a rectangular wire frame. The frame is held vertically so that the film drains downward and forms a wedge with flat faces. The thickness of the film at the top is essentially zero. The film is viewed in reflected white light with near-normal incidence, and the first violet ( = 420 nm) interference band is observed 3.00 cm from the top edge of the film. (a) Locate the first red ( = 680 nm) interference band. (b) Determine the film thickness at the positions of the violet and red bands. (c) What is the wedge angle of the film?
An effect analogous to two-slit interference can occur with sound waves, instead of light. In an open field, two speakers placed 1.30 m apart are powered by a single-function generator producing sine waves at 1200-Hz frequency. A student walks along a line 12.5 m away and parallel to the line between the speakers. She hears an alternating pattern of loud and quiet, due to constructive and destructive interference. What is (a) the wavelength of this sound and (b) the distance between the central maximum and the first maximum (loud) position along this line?