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Converging lenses, diffraction grating, reflection, three polarizing sheets, un-polarized light

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1) Two converging lenses with focal lengths of 40cm and 20cm are placed 10cm apart. A 2cm tall object is 15cm from the 40cm focal length lens.
a) Use ray tracing to locate the image of the lens combination.
b) Is the image real or virtual? Is it upright or inverted?
c) Calculate the exact location and height of the image.

2) A diffraction grating is placed 1m from a viewing screen. Light from a hydrogen lamp goes through the grating. A hydrogen spectral line with a wavelength of 656nm is seen 60cm to one side of the center. The n the hydrogen lamp is replaced with a mercury lamp. Mercury has a spectral line with a wavelength of 546nm.
a) Where is this line seen on the screen?
b) A spectral line is seen on the screen 36.4cm away from the center. What is the wavelength?

3) In the figure, a glass lens is coated on one side with a thin film of magnesium fluoride to reduce reflection from the surface. The index of refraction for magnesium fluoride is 1.38; that for glass is 1.50. what is the least coating thickness that eliminates (via interference) the reflections at the middle of the visible spectrum ( wavelength = 550nm), assuming that the lights are approximately perpendicular to the lens surface.

4) The figure shows a system of three polarizing sheets in the path of initially un-polarized light. The polarizing direction of the first sheet is parallel to the y-axis, that of the second sheet is 60 degrees counter clockwise from the y-axis and th
at of the third sheet is parallel to the x-axis. What fraction of the initial intensity of the light emerges from the system, and how is it polarized?

5) The figure shows four pairs of polarizing sheets seen face-on. Each pair is mounted in the path of initially un-polarized light. The polarizing direction of each sheet (indicated by the straight line) is referenced to either a horizontal x-axis or a vertical y-axis. Arrange them according to the fraction of the initial intensity that they pass in greatest first.

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