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

See attachment for figures.

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 that 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.

Attachments

Solution Preview

Please refer to the attached file.

1) Refer to the other attached file for the ray tracing diagram

a) each horizontal division represents 5 cm. The lens on the left is your first lens with focal length 40 cm. Its object is located 15 cm to the left of the first lens in solid blue arrow.
b) The first ray is drawn from the tip of the solid blue arrow to the lens and then through the focal point, f1. The second ray is drawn thru the principal axis at the lens.
c) The intersection point is where the image is located. It's shown with a blue dotted arrow.
d) Now, this dotted blue arrow serves as an object for the second converging lens.
e) The first ray is drawn from the tip of the dotted blue arrow to the lens and then through the focal point, f2. The second ray is drawn thru ...

Solution Summary

The solution presents full calculations, formulas and explanations in solving the problems regarding converging lenses, diffraction grafting, reflection and polarizing.

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