# Examples Wave Optics.

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Examples Wave Optics

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?

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?

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

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?

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.

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.

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?

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.

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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