A source containing a mixture of hydrogen and deuterium atoms emits light at two wavelengths whose mean is 453 nm and whose separation is 0.226 nm. Find the minimum number of lines needed in a diffraction grating that can resolve these lines in the first order. Number i Units nTouthoolc and Modia

A source containing a mixture of hydrogen and deuterium atoms emits light at two wavelengths whose mean is 453 nm and whose separation is 0.226 nm. Find the minimum number of lines needed in a diffraction grating that can resolve these lines in the first order. Number i Units nTouthoolc and Modia

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter36: Applications Of The Wave Model

Section: Chapter Questions

Problem 42PQ

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A beam of bright red light of wavelength 654 nm passes through a diffraction grating Enclosing the space beyond the grating is a large semicylindrical screen centered on the grating, with its axis parallel to the slits in the grating. Fifteen bright spots appear on the screen. Find (a) the maximum and (b) the minimum possible values for the slit separation in the diffraction grating.
From Equation 37.2, find an expression for the sine of the angles at which the minimum intensity occurs in a single-slit diffraction pattern. Compare the result to Equation 37.1.
A chamber 5.0 cm long with flat, parallel windows at the ends is placed in one arm of a Michelson interferometer (see below). The light used has a wavelength of 500 nm in a vacuum. While all the air is being pumped out of the chamber, 29 fringes pass by a point on the observation screen. What is the refractive index of the air?
Consider a light wave passing through a slit and propagating toward a distant screen. Figure P37.53 shows the intensity variation for the pattern on the screen. Give a mathematical argument that more than 90% of the transmitted energy is in the central maximum of the diffraction pattern. Suggestion: You are not expected to calculate the precise percentage, but explain the steps of your reasoning. You may use the identification 112+132+152+=28 Figure P37.53
In Figure 38.4, assume the slit is in a barrier that is opaque to x-rays as well as to visible light. The photograph in Figure 38.4b shows the diffraction pattern produced with visible light. What will happen if the experiment is repeated with x-rays as the incoming wave and with no other changes? (a) The diffraction pattern is similar. (b) There is no noticeable diffraction pattern but rather a projected shadow of high intensity on the screen, having the same width as the slit. (c) The central maximum is much wider, and the minima occur at larger angles than with visible light. (d) No x-rays reach the screen.
Calculate the wavelength of light that has its third minimum at an angle of 30.0° when falling on double slits separated by 3.00 m. Explicitly show how you follow the steps from the Problem-Solving Strategy: Wave Optics, located at the end of the chapter.
Suppose Youngs double-slit experiment is performed in air using red light and then the apparatus is immersed in water. What happens to the interference pattern on the screen? (a) It disappears. (b) The bright and dark fringes stay in the same locations, but the contrast is reduced. (c) The bright fringes are closer together. (d) The bright fringes are farther apart. (e) No change happens in the interference pattern.
A soap bubble is blown outdoors. What colors (indicate by wavelengths) of the reflected sunlight are seen enhanced? The soap bubble has index of refraction 1.36 and thickness 380 nm.
Many cells are transparent anti colorless. Structures of great interest in biology and medicine can be practically invisible to ordinary microscopy. To indicate the size and shape of cell structures, an interference micro-scope reveals a difference in index of refraction as a shift in interference fringes. The idea is exemplified in the following problem. An air wedge is formed between two glass plates in contact along one edge and slightly separated at the opposite edge as in Figure P37.37. When the plates are illuminated with monochromatic light from above, the reflected light has 85 dark fringes. Calculate the number of dark fringes that appear if water (n = 1.33) replaces the air between the plates.
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) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width 20.0 m. (b) What slit width would place this minimum at 85.0°? Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics
Four trials of Young's double-slit experiment are conducted. (a) In the first trial, blue light passes through two fine slits 400 m apart and forms an interference pattern on a screen 4 in away, (b) In a second trial, red light passes through the same slits and falls on the same screen. (c) A third trial is performed with red light and the same screen, but with slits 800 m apart, (d) A final trial is performed with red light, slits 800 m apart, and a screen 8 m away. (i) Rank the trials (a) through (d) from the largest to the smallest value of the angle between the central maximum and the first-order side maximum. In your ranking, note any cases of equality, (ii) Rank the same trials according to the distance between the central maximum and the First-order side maximum on the screen.