For the following questions, assume the wavelengths of visible light range from 380 nm to 760 nm in a vacuum. (a) What is the smallest separation (in nm) between two slits that will produce a seventh-order maximum for any visible light? nm (b) What is the smallest separation (in nm) between two slits that will produce a seventh-order maximum for all visible light? nm

For the following questions, assume the wavelengths of visible light range from 380 nm to 760 nm in a vacuum. (a) What is the smallest separation (in nm) between two slits that will produce a seventh-order maximum for any visible light? nm (b) What is the smallest separation (in nm) between two slits that will produce a seventh-order maximum for all visible light? nm

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter36: Wave Optics

Section: Chapter Questions

Problem 4P: In a Youngs double-slit experiment, two parallel slits with a slit separation of 0.100 mm are...

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An American standard analog television picture (non-HDTV), also known as NTSC, is composed of approximately 485 visible horizontal lines of varying light intensity. Assume your ability to resolve the lines is limited only by the Rayleigh criterion, the pupils of your eyes are 5.00 min in diameter, and the average wavelength of the light coming from the screen is 550. nm. Calculate the ratio of the minimum viewing distance to the vertical dimension of the picture such that you will not be able to resolve the lines.
In a Youngs double-slit experiment, a set of parallel slits with a separation of 0.100 mm is illuminated by light having a wave- length of 589 nm, and the interference pattern is observed on a screen 4.00 m from the slits, (a) What is the difference in path lengths from each of the slits to the location of a third-order bright fringe on the screen? (b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern?
Coherent light of wavelength 501.5 nm is sent through two parallel slits in an opaque material. Each slit is 0.700 m wide. Their centers are 2.80 m apart. The light then falls on a semicylindrical screen, with its axis at the midline between the slits. We would like to describe the appearance of the pattern of light visible on the screen. (a) Find the direction for each two-slit interference maximum on the screen as an angle away from the bisector of the line joining the slits. (b) How many angles are there that represent two-slit interference maxima? (c) Find the direction for each single-slit interference minimum on the screen as an angle away from the bisector of the line joining the slits. (d) How many angles are there that represent single-slit interference minima? (e) How many of the angles in part (d) are identical to those in part (a)? (f) How many bright fringes are visible on the screen? (g) If the intensity of the central fringe is Imax, what is the intensity of the last fringe visible on the screen?
(a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of 20.0°? (b) At what angle will the fourth line of the Balmer series appear in first order? (c) At what angle will the second-order maximum be for the first line?
Light of wavelength 632.8 nm illuminates a single slit, and a diffraction pattern is formed on a screen 1.00 m from the slit. (a) Using the data in the following table, plot relative intensity versus position. Choose an appropriate value for the slit width a and, on the same graph used for the experimental data, plot the theoretical expression for the relative intensity IImax=sin22 where = (a sin )/. (b) What value of a gives the best fit of theory and experiment? Position Relative to Maximum (mm) Relative Intensity 0 1.00 0.8 0.95 1.6 0.80 3.2 0.39 4.8 0.079 6.5 0.003 8.1 0.036 9.7 0.043 11.3 0.013 12.9 0.000 3 14.5 0.012 16.1 0.015 17.7 0.004 4 19.3 0.000 3
In a Youngs double-slit experiment, a set of parallel slits with a separation of 0.100 mm is illuminated by light having a wave- length of 589 nm, and the interference pattern is observed on a screen 4.00 m from the slits, (a) What is the difference in path lengths from each of the slits to the location of a third-order bright fringe on the screen? (b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern?
A spacer is cut from a playing card of thickness 2.90 104 m and used to separate one end of two rectangular, optically flat. 3.00-cm long glass plates with n = 1.55, as in Figure P24.24. Laser light at 594 nm shine straight down on the top plate. The plates have a length of 3.00 cm. (a) Count the number of phase reversals for the interfering waves. (b) Calculate the separation between dark interference Kinds observed on the lop plate.
In Figure P27.7 (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?
(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 m. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.
In a Youngs double-slit experiment, two parallel slits with a slit separation of 0.100 mm are illuminated by light of wavelength 589 nm, and the interference pattern is observed on a screen located 4.00 m from the slits. (a) What is the difference in path lengths from each of the slits to the location of the center of a third-order bright fringe on the screen? (b) What is the difference in path lengths from the two slits to the location of the center of the third dark fringe away from the center of the pattern?
Two closely spaced wavelengths of light are incident on a diffraction grating. (a) Starting with Equation 37.7, show that the angular dispersion of the grating is given by dd=mdcos (b) A square grating 2.00 cm on each side containing 8 000 equally spaced slits is used to analyze the spectrum of mercury. Two closely spaced lines emitted by this element have wavelengths of 579.065 nm and 576.959 nm. What is the angular separation of these two wavelengths in the second-order spectrum?
Light of wavelength 587.5 nm illuminates a slit of width 0.75 mm. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.85 mm from the central maximum? (b) Calculate the width of the central maximum.