Exam 19: Optical Instruments

You have a choice between two lenses of focal lengths f_a and f_b, where f_b = 2f_a, to use as the objective lens in building a compound microscope. If the magnification you obtain using lens a is M_a, what will be the magnification when using lens b?

A camera with a 20-cm diameter lens is recording images using a filter that allows only light of wavelength 600 nm to pass through. (a) What is the limit on the angular resolution (in microradians) in this case? (b) What is the diameter of the minimum-sized features that could be resolved on Mars with this camera? The distance to Mars at the time is 9.0 × 10⁷ km.

The world's largest refracting telescope is operated at the Yerkes Observatory in Wisconsin. It has an objective lens of diameter of 1.02 m. Suppose such an instrument were mounted on a satellite at an elevation of 300 km above the ground and used to map surface details. If the telescope is forming images with light of wavelength 550 nm, what is the minimum separation of two objects on the ground whose separation could be clearly resolved by this lens?

Which one of the following is normally not a characteristic of a simple two-lens refracting astronomical telescope?

A camera used for aerial mapping has a lens with a 30-cm diameter maximum aperture and a 42-cm focal length. Light of 550 nm wavelength is used to form the image. Assuming that the resolution of the camera is limited only by diffraction, what is the smallest angle (in milliradians) subtended by an object on the ground that can be resolved by this camera at maximum aperture?

A camera lens having a 50-mm focal length is set to f/4.0. What is the minimum spacing of two objects located 12 m from the lens if the objects are just barely resolved in the image using light of wavelength 500 nm?

A person having a near point of 25 cm uses a magnifying glass with a focal length of 10 cm. What is the angular magnification of the glass for that person when her eyes are focused at infinity?

The focal lengths of the objective lens and the eyepiece in a microscope are 2.90 mm and 2.50 cm, respectively. An object is placed 3.00 mm from the objective. The image of this object is viewed with the eyepiece adjusted for minimum eyestrain for persons with a near point of 25 cm. What is the distance between the objective and the eyepiece?

Which one of the following statements is correct?

What is the power of the lens that has a focal length of 40 cm and a diameter if 5.0 cm?

A person uses a converging lens of focal length 5.0 cm as a magnifying glass. What is the angular magnification if the person's eye is relaxed and has a near point of 25 cm?

As a treatment for cataracts (a cloudiness of the lens of the eye), the natural lens is removed and a plastic lens is implanted. After this is done a person can see distant objects clearly, but he cannot accommodate to focus on nearby objects. If such a person wanted to read a book at a distance of 25 cm, he would have to wear contact lenses having a diopter power of

The objective lens of a telescope has a focal length of 2.0 m and its eyepiece has a focal length of 1.0 cm. What is the magnification of this telescope when viewing Jupiter?

A compound microscope consists of an objective lens of focal length f₀ and an eyepiece that by itself produces an angular magnification 25.0. The microscope is designed so that the object to be viewed is on the left side of the objective lens and is focused in a plane that is 28.00 cm away from the right-hand (or inside) focal point of the objective lens. When properly adjusted, the eyepiece and the objective lens are 29.90 cm apart. The eyepiece magnification is based on an image at infinity and a near point at 25.0 cm. What is f₀?

Even with perfect optics, what is the resolution limit (in radians) of the Hubble Space Telescope when it is focusing light of wavelength 400 nm? The mirror diameter is 2.4 m.

Chromatic aberration in lenses is due to the

In a compound microscope

A person is designing a telescope with a magnification of 10. If the telescope is limited to a length of 0.20 m, what is the approximate focal length of the objective?

A little known fact is that both Robinson Crusoe and Friday wore eyeglasses. As it so happens, Robinson Crusoe was farsighted while Friday was nearsighted. Whose eyeglasses did they use whenever they wanted to start a fire by focusing the sun's rays?

A nearsighted man wears contact lenses of -3.00 diopters. With these lenses, his corrected near point is 25.0 cm. What is his uncorrected near point?