Question 9 of 15 A thin layer of oil (n = 1.25) covers the surface of a puddle of water (n = 1.33). If light of wavelength 500 nm in vacuum is minimally reflected (film appears dark) from the oil surface, what is the minimum non-zero thickness of the oil? 500 nm 400 nm 300 nm 200 nm 100 nm 0000

Question 9 of 15 A thin layer of oil (n = 1.25) covers the surface of a puddle of water (n = 1.33). If light of wavelength 500 nm in vacuum is minimally reflected (film appears dark) from the oil surface, what is the minimum non-zero thickness of the oil? 500 nm 400 nm 300 nm 200 nm 100 nm 0000

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 37PQ

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Slit 1 of a double-slit is wider than slit 2 so that the light from slit 1 has an amplitude exactly 3 times that of the light from slit 2. Show that Equation 36.9 is replaced by the following equation for this situation: I=Imax[1+3cos2(dsin)] 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=3E0sintE2=E0sin(t+) The phase angle in E2 is due to the extra path length traveled by the lower beam in Figure 36.4. 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 might find the following trigonometric identities helpful: sinA+sinB=2sin(A+B2)cos(AB2)sin(A+B)=sinAcosB+cosAsinBcosA=2cos2(A2)1
(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.
Green light has a wavelength of 500 nm in air. (i) Assume green light is reflected from a mirror with angle of incidence 0. The incident and reflected waves together constitute a standing wave with what distance from one node to the next node? (a) 1000 nm (b) 500 nm (c) 250 nm (d) 125 nm (e) 62.5 nm (ii). The green light is sent into a Michelson interferometer that is adjusted to produce a central bright circle. How far must the interferometer's moving mirror be shifted to change the center of the pattern into a dark circle? Choose from the same possibilities as in part (i). (iii). The green light is reflected perpendicularly from a thin film of a plastic with an index of refraction 2.00. The film appears bright in the reflected light. How much additional thickness would make the film appear dark?
A student sets up a double-slit experiment using mono chromatic light of wavelength . The distance between the slits is equal to 25 . (a) Find the angles at which the m = 1, 2, and 3 maxima occur on the viewing screen. (b) At what angles do the first three dark fringes occur? (c) Why are the answers so evenly spaced? Is the spacing even for all orders? Explain.
Monochromatic light is beamed into a Michelson interferometer. The movable mirror is displaced 0.382 mm, causing the central spot in the interferometer pattern to change from bright to dark and back to bright N = 1 700 times. (a) Determine the wavelength of the light. What color is it? (b) If monochromatic red light is used instead and the mirror is moved the same distance, would N be larger or smaller? Explain.
A student sets up a double-slit experiment using mono chromatic light of wavelength . The distance between the slits is equal to 25 . (a) Find the angles at which the m = 1, 2, and 3 maxima occur on the viewing screen. (b) At what angles do the first three dark fringes occur? (c) Why are the answers so evenly spaced? Is the spacing even for all orders? Explain.
Monochromatic light is beamed into a Michelson interferometer. The movable mirror is displaced 0.382 mm, causing the central spot in the interferometer pattern to change from bright to dark and back to bright N = 1 700 times. (a) Determine the wavelength of the light. What color is it? (b) If monochromatic red light is used instead and the mirror is moved the same distance, would N be larger or smaller? Explain.
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
Light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at 32.0, (a) what is the number of rulings per centimeter for the grating? (b) Determine the total number of primary maxima that can be observed in this situation.
Introduction to Optics; a) Explain the experiment represented in figures given below. Write the names of the interferences. b) A pair of screens are placed 13.7m apart. A third order fringe is seen on the screen 2.50cm from the central fringe. If the slits were cut 0.0960 cm apart, determine the wavelength of this light. Roughly what colour is it? L= 13.7 m, n=3, x=2.5 cm, d=0.096 cm,λ= xd/nL
A Michelson interferometer uses light from a sodium lamp. Sodium atoms emit light having wavelengths 589.0 nm and 589.6 nm. The interferometer is initially set up with both arms of equal length (i.e., L1 = L2), producing a bright spot at the center of the interference pattern. How far must mirror M2 be moved so that one wavelength has produced one more new maximum than the other wavelength?
Chapter 27: Problem 1: Consider a 465nm wavelength blue light falling on a pair of slits separated by 0.075 mm. 1) At what angle (in degrees) is the first-order maximum for the blue light?