A thin layer of oil with index of refraction n, = 1.47 is floating above thewater. The index of refraction of water is n, =1.3. The index of refraction of air is n, = 1. A light|with wavelength À = 725 nm goes in from the air to oil and water.(a) Express the wavelength of the light in the oil, d,, in terms of å and n„.n.n.n.(b) Express the minimum thickness of the film that will result in destructive interference, fmin, in terms of 7g.(c) Express 1min in terms of 2 and n,.(d) Solve for the numerical value of tmin in nm.

Given that: Given that:Refractive index of oil, no=1.47 Refractive index of water, nw=1.3Refractive…

Answered: A thin layer of oil with index of…

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter22: Reflection And Refraction Of Light

Section: Chapter Questions

Problem 30P: The index of refraction for crown glass is 1.512 at a wavelength of 660 nm (red), whereas its index...

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If a microscope can accept light from objects at angles as large as =70 , what is the smallest structure that can be resolved when illuminated with light of wavelength 500 nm and (a) the specimen is in air? (b) When the specimen is immersed in oil, with index of refraction of 1.52?
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.
To save money on making military aircraft invisible to radar, an inventor decides to coat them with a nonreflective material having an index of refraction of 1.20, which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers. (a) What thickness should the coating be to inhibit the reflection of 4.00-cm wavelength radar? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
Two polarizing sheets P1 and P2 are placed together with their transmission axes oriented at an angle to each other. What is when only 25% of the maximum transmitted light intensity passes through them?
Light enters a prism of crown glass and refracts at an angle of 5.00 with respect to the normal at the interface. The crown glass has a mean index of refraction of 1.51. It is combined with one flint glass prism (n = 1.65) to produce no net deviation. a. Find the apex angle of the flint glass. b. Assume the index of refraction for violet light (v = 430 nm) is nv = 1.528 and the index of refraction for red light (r = 768 nm) is nr = 1.511 for crown glass. For flint glass using the same wavelengths, nv = 1.665 and nr = 1.645. Find the net dispersion.
Components of some computers communicate with each other through optical fibers having an index of refraction n = 1.55. What time in nanoseconds is required for a signal to travel 0.200 m through such a fiber?
If the light source in the preceding problem is changed, the angular position of the third maximum is found to be 0.57°. What is the wavelength of light being used now?
A film of soapy water (n=1.33) on top of a plastic cutting board has a thickness of 233 nm. What color is most strongly reflected if it is illuminated perpendicular to its surface?
A film of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths? Oil has an index of refraction of 1.40.
Check Your Understanding Although m, the number of fringes observed, is an integer, which is often regarded as having zero uncertainty, in practical terms, it is all too easy to lose track when counting fringes. In Example 3.6, if you estimate that you might have missed as many as five fringes when you reported m=122 fringes, (a) is the value for the index of refraction worked out in Example 3.6 too large or too small? (b) By how much?
Figure 3.14 shows two 7.50-cm-long glass slides illuminated by pure 589-nm wavelength light incident perpendicularly. The top slide touches the bottom slide at one end and rests on some debris at the other end, forming a wedge of air. How thick is the debris, if the dark bands are 1.00 mm apart? Figure 3.14 (a) The rainbow-color bands are produced by thin-film interference in the air between the two glass slides. (b) Schematic of the paths taken by rays in the wedge of air between the slides. (c) If the air wedge is illuminated with monochromatic light, bright and dark bands are obtained rather than repeating rainbow colors.
What is the wavelength of light falling on double slits separated by 2.00 m if the third-order maximum is at an angle of 60.0° ?

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