Learning Materials
Features
Discover
Chapter 33: Q. 12 (page 955)
A diffraction grating is illuminated simultaneously with red light of wavelengthand light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light. What is the unknown wavelength
The unknown wavelength is.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
FIGURE shows two nearly overlapped intensity peaks of the sort you might produce with a diffraction grating . As a practical matter, two peaks can just barely be resolved if their spacing equals the width w of each peak, where is measured at half of the peak鈥檚 height. Two peaks closer together than will merge into a single peak. We can use this idea to understand the resolution of a diffraction grating.
a. In the small-angle approximation, the position of the peak of a diffraction grating falls at the same location as the fringe of a double slit: . Suppose two wavelengths differing by pass through a grating at the same time. Find an expression for localid="1649086237242" , the separation of their first-order peaks.
b. We noted that the widths of the bright fringes are proportional to localid="1649086301255" , where localid="1649086311478" is the number of slits in the grating. Let鈥檚 hypothesize that the fringe width is localid="1649086321711" Show that this is true for the double-slit pattern. We鈥檒l then assume it to be true as localid="1649086339026" increases.
c. Use your results from parts a and b together with the idea that localid="1649086329574" to find an expression for localid="1649086347645" , the minimum wavelength separation (in first order) for which the diffraction fringes can barely be resolved.
d. Ordinary hydrogen atoms emit red light with a wavelength of localid="1649086355936" In deuterium, which is a 鈥渉eavy鈥� isotope of hydrogen, the wavelength is localid="1649086363764" What is the minimum number of slits in a diffraction grating that can barely resolve these two wavelengths in the first-order diffraction pattern?
Light of wavelength passes though two slits separated by and is observed on a screen behind the slits. The location of the central maximum is marked on the screen and labeled
a. At what distance, on either side of , are the bright fringes?
b. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by in comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay?
c. With the glass in place, what is the phase difference between the two waves as they leave the slits?
d. The glass causes the interference fringe pattern on the screen to shift sideways. Which way does the central maximum move (toward or away from the slit with the glass) and by how far?
The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing. If the melanin lines on the wing are spaced apart, what is the first-order diffraction angle for green light ?
FIGURE P33.49 shows the interference pattern on a screen behind a diffraction grating. The wavelength of the light is . How many lines per millimeter does the grating have?
You've found an unlabeled diffraction grating. Before you can use it, you need to know how many lines per it has. To find out, you illuminate the grating with light of several different wavelengths and then measure the distance between the two first-order bright fringes on a viewing screen behind the grating. Your data are as follows:
Use the best-fit line of an appropriate graph to determine the number of lines per .
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine