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Examples Wave Optics

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1- A double-slit experiment is set up using a helium-neon laser ( λ = 633 nm). Then a very thin piece of glass ( n= 1.50 ) is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the m = 10 dark fringe. How thick is the glass?

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2- Light of wavelength 600 nm passes through a double slit and is viewed on a screen 2.0 m behind the slits. Each slit is mm wide and they are separated by mm. How many bright fringes are seen on the screen?

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3- Light consisting of two nearly equal wavelengths λ +λ and λ, where λ << λ , is incident on a diffraction grating. The slit separation of the grating is d. Show that the angular separation of these two wavelengths in the mth order is

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**b. sodium atoms emit light at 589. 0 nm and 589. 6 nm**

b. sodium atoms emit light at nm and nm. What are the first-order and second-order angular separations ( in degrees) of these two wavelengths for a 600 line/mm grating?

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4- The 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 y equals the width w of each peak, where w is measured at half of the peak’s height. Two peaks closer together than w will merge into a single peak. We can use this idea to understand the resolution of diffraction grating. In small angle approximation, the position of the m=1 peak of diffraction grating falls at the same location as the m =1 fringe of a double slit: y1 = λL/d. Suppose two wavelengths differing by λ pass through a grating at the same time. Find an expression for y, the separation of their first-order peaks.

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B. We noted that the widths of the bright fringes are proportional to 1/N, where N is the number of slits in the grating. Let’s hypothesize that the fringe width is w = y1 / N. Show that this is true for the double-slit pattern. We’ll then assume it to be true as N increases.

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c. Use your results from parts a and b together with the idea that ymin = w to find an expression for λmin, 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 nm. In deuterium, which is a “heavy” isotope of hydrogen, the wavelength is nm. What is the minimum number of slits in a diffraction grating that can barely resolve these two wavelengths in the first-order diffraction pattern?

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**5. The Figure shows a plane wave approaching a diffraction grating at angle .**

Show that the angles m for constructive interference are given by the grating equation Angles are considered positive if they are above the horizontal line, negative if below it.

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b. The two first-order maxima, m = +1 and m = -1, are no longer symmetrical about the center. Find 1 and -1 for 500 nm light incident on a 600 line/mm grating at = 30.

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Interference & Diffraction

Interference & Diffraction

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