Chapter 35: Q.6 (page 1016)
A friend lends you the eyepiece of his microscope to use on your own microscope. He claims the spatial resolution of your microscope will be halved, since his eyepiece has the same diameter as yours but twice the magnification. Is his claim valid? Explain.
Claim is not valid.
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The Hubble Space Telescope has a mirror diameter of 2.4 m. Suppose the telescope is used to photograph stars near the center of our galaxy, 30,000 light years away, using red light with a wavelength of 650 nm.
a. Whatโs the distance (in km) between two stars that are marginally resolved? The resolution of a reflecting telescope is calculated exactly the same as for a refracting telescope.
b. For comparison, what is this distance as a multiple of the distance of Jupiter from the sun?
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 sunโs 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 mm. Your calculations indicate that the laser must be focused to a 5.0@mm@diameter spot in order to have sufficient power to make the cut. What is the minimum diameter of the lens you must install?
Your task in physics laboratory is to make a microscope from two lenses. one lens has a focal length of the other objective, and you want the eyepiece to be from the objective.
(a). For viewing with a relaxed eye, how far should the sample be from the objective lens?
(b). What is the magnification of your microscope?
The lens shown in FIGURE CP is called an achromatic doublet, meaning that it has no chromatic aberration. The left side is flat, and all other surfaces have radii of curvature R.
a. For parallel light rays coming from the left, show that the effective focal length of this two-lens system is , where localid="1648757054673" and are, respectively, the indices of refraction of the diverging and the converging lenses. Donโt forget to make the thin-lens approximation.
b. Because of dispersion, either lens alone would focus red rays and blue rays at different points. Define and as for the two lenses. What value of the ratio makes for the two-lens system? That is, the two-lens system does not exhibit chromatic aberration.
c. Indices of refraction for two types of glass are given in the table. To make an achromatic doublet, which glass should you use for the converging lens and which for the diverging lens? Explain
Crown glass 1.525 1.517
Flint glass 1.632 1.616
d. What value of R gives a focal length of ?
Yang can focus on objects away with a relaxed eye. With full accommodation, she can focus on objects away. After her eyesight is corrected for distance vision, what will her near point be while wearing her glasses?
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