What is the distance between three dark fringes when a light with wavelength20nm shines through a slit of length 40mm onto a wall 2.5m away? *1.1 x 10-3mO 3.1 x 10-3m3.1 x 10-6mO 1.1 x 10-5mif you know the focal length of concave mirror = 15 cm and the position of screen= 67 cm where place the mirror? *72cm75 cm52 cm

The distance of any dark fringe is given in terms of wavelength, distance from slits, and distance…

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What is the distance between three dark fringes when a light with wavelength 20nm shines through a slit of length 40mm onto a wall 2.5m away? O 1.1 x 10-3m 3.1 x 10-3m O 3.1 x 10-6m O 1.1 x 10-5m

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter27: Wave Optics

Section: Chapter Questions

Problem 50PE: (a) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width 20.0...

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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.
The Very Large Array (VLA) is a set of 27 radio telescope dishes in Catron and Socorro counties, New Mexico (Fig. P37.37). The antennas can be moved apart on railroad tracks, and their combined signals give the resolving power of a synthetic aperture 36.0 km in diameter. (a) If the detectors are tuned to a frequency of 1.40 GHz, what is the angular resolution of the VLA? (b) Clouds of interstellar hydrogen radiate at the frequency used in part (a). What must be the separation distance of two clouds at the center of the galaxy, 26 000 light-years away, if they are to be resolved? (c) What If? As the telescope looks up, a circling hawk looks down. Assume the hawk is most sensitive to green light having a wavelength of 500 nm and has a pupil of diameter 12.0 mm. Find the angular resolution of the hawks eye. (d) A mouse is on the ground 30.0 m below. By what distance must the mouses whiskers be separated if the hawk can resolve them? Figure P37.37
A diffraction grating has a second-order resolving power of 1 250. (a) Find the number of illuminated lines on the grating. (b) Calculate the smallest difference in wavelengths surrounding 525 nm that can be resolved in the first-order diffraction pattern.
(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
One leg of a Michelson interferometer contains an evacuated cylinder of length L, having glass plates on each end. A gas is slowly leaked into the cylinder until a pressure of 1 atm is reached. If N bright fringes pass on the screen during this process when light of wavelength A is used, what is the index of refraction of the gas? Hint: The fringe shifts occur because the wavelength of the light changes inside the gas-filled tube.
Unreasonable Results An amateur astronomer wants to build a telescope with a diffraction limit that will allow him to see if there are people on the moons of Jupiter. (a) What diameter mirror is needed to be able to see 1.00 m detail on a Jovian Moon at a distance of 7.50108 km from Earth? The wavelength of light averages 600 nm. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
A diffraction grating has a second-order resolving power of 1 250. (a) Find the number of illuminated lines on the grating. (b) Calculate the smallest difference in wavelengths surrounding 525 nm that can be resolved in the first-order diffraction pattern.
An air wedge is formed between two glass plates separated at one edge by a very fine wire of circular cross section as shown in Figure P37.37. When the wedge is illuminated from above by 600-nm light and viewed from above, 30 dark fringes are observed. Calculate the diameter d of the wire.
The limit to the eye's acuity is actually related to diffraction by the pupil. (a) What is the angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 550 nm? (b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.30 m apart? (c) What is the distance between two just-resolvable points held at an arm's length (0.800 m) from your eye? (d) How does your answer to (c) compare to details you normally observe in everyday circumstances?
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.
Figure CQ37.2 shows an unbroken soap film in a circular frame. The film thickness increases from lop 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?
(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.