Exam 2 practice problems solutions

# Take 2 converging lenses and place them at the ends

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Take 2 converging lenses and place them at the ends of a tube (part ‘a’ of the diagram). Place the object to the left of the tube. You will look through the tube from the right. The object to be magnified needs to be placed outside of the focal point of the objective lens so it will form a real image (part ‘b’ of the diagram). The eyepiece lens needs to be placed so that the image from the objective lens is just inside its focal point. This will cause an inverted, virtual, and highly magnified final image to be formed. 19. Jewelers use a special magnifying device when inspecting gems for authenticity or defects. This device consists of a hollow cylinder, open at one end and fitted with a converging lens on the other. The jeweler places the gem on a glowing pad then covers the gem with the cylinder. (Meaning, the gem is effectively at the end of the cylinder opposite the lens.) The jeweler then looks at the gem through the lens and sees a highly magnified image of the gem.

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Suppose you are a jeweler using one of these devices to identify some potentially fake gems. You suspect that you will need a device that magnifies at least 50 times in order to make a confident decision about the gems. Your current device is a cylinder 5.0 cm high and is fitted with a lens of focal length 5.6 cm . a. Draw a ray diagram showing how this device achieves such a large magnification. Note: Your diagram doesn’t have to be to scale, but it does have to be qualitatively accurate, meaning the image must have the correct properties. b. Is your current device sufficient for the task? Show in detail how you determined this. c. If your device is not sufficient, explain what you would do to modify it so that it is. If your device is sufficient, explain how you could improve its magnification ability even further. With the gem just inside the focal point of a converging lens, a highly magnified, upright, virtual image will be formed. 1 1 1 1 i o o o d m d d f d     1 1 1 1 9.33 5.0 5.6 5.0 m cm cm cm   This magnification is far too low to be able to detect the counterfeit nature of the gems. To fix this the cylinder needs to be extended so the gem is closer to the focal point of the lens. To determine how much I’ll solve the above equation for o d . 1 1 1 1 1 1 1 5.6 1 5.49 50 o o o m d f d d f cm cm m   So, as long as the cylinder is between 5.49 and 5.6cm the magnifier will be able to detect the counterfeit nature of the gems. 20. If you look at the passenger side mirror of most cars you will see the following warning printed on the bottom of the mirror: “Objects in mirror are closer than they appear.” a. What kind of mirror is it? Draw ray diagrams to justify your answer.
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