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07:46A microscope with a tube length of 180 mm achieves a total magnification of 800x with a 40x objective and a 20x eyepiece. The microscope is focused for viewing with a relaxed eye. Approximately how far is the sample from the objective lens?
A simple and relatively inexpensive microscope eyepiece is the Ramsden eyepiece shown in FIGURE P35.40. Two plano-convex lenses have their curved surfaces facing each other, which a more advanced analysis shows is the orientation that minimizes spherical aberration. That same analysis finds that chromatic aberration is minimized with lens spacing L = 1/2 (f₁ + f₂). Your task is to design a 10x Ramsden eyepiece in which the first lens has a focal length of 30 mm. What are (a) the focal length and (b) the spacing of the second lens?
Mars (6800 km diameter) is viewed through a telescope on a night when it is 1.1 x 10⁸ km from the earth. Its angular size as seen through the eyepiece is 0.50°, the same size as the full moon seen by the naked eye. If the eyepiece focal length is 25 mm, how long is the telescope?
White light is incident onto a 30° prism at the 40° angle shown in FIGURE P35.41. Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is 2.0% larger than the index of refraction of red light. At what angle Φ does red light emerge from the rear face?
Marooned on a desert island and with a lot of time on your hands, you decide to disassemble your glasses to make a crude telescope with which you can scan the horizon for rescuers. Luckily you’re farsighted, and, like most people, your two eyes have different lens prescriptions. Your left eye uses a lens of power +4.5 D, and your right eye’s lens is +3.0 D. Which lens should you use for the objective and which for the eyepiece? Explain.
High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun's light to a small spot that can burn things. As an engineer, you have designed a laser cutting device in which the material to be cut is placed 5.0 cm behind the lens. You have selected a high-power laser with a wavelength of 1.06 μm. Your calculations indicate that the laser must be focused to a 5.0-μm-diameter spot in order to have sufficient power to make the cut. What is the minimum diameter of the lens you must install?
