Exam 25: Optical Instruments

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?

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

What is the power of a lens that has a focal length of -40 cm and a width of 2.0 cm?

Mahmood is farsighted and cannot see objects clearly that are closer to his eye than 80.0 cm. What is the focal length of the contact lenses that will enable him to comfortably see objects at a distance Of 25.0 cm from his eyes?

Given perfect lenses, what is the main reason that a telescope with a large-diameter objective lens can produce a sharper image than one with a small-diameter lens?

The distance between the object to be viewed and the eyepiece of a compound microscope is 18.0 cm. The focal length of its objective lens is 0.80 cm and the eyepiece has a focal length of 2.3 cm. The near-point distance of the person using the microscope is 25.0 cm. What is the magnitude of The total magnification of the microscope if it is designed for minimum eyestrain?

Suppose your telescope has perfect mirrors and is limited only by diffraction. If you are viewing with light of $400 \mathrm {~nm}$ wavelength, what diameter mirror in a space telescope would have $1.0 - \mathrm { km }$ resolution of objects on Mars when viewed from above the earth at a time when the Earth-Mars distance of 80 million kilometers?

What power contact lens should be used to correct the vision of a farsighted person whose near point is 80 cm so she can see things clearly that are 25 cm in front of her?

A certain astronomical telescope has a diameter of $5.60 \mathrm {~m}$ . What is the minimum angle of resolution for this telescope when it is forming images using light of wavelength $620 \mathrm {~nm}$ ?

When a person with a near point at 28 cm uses a certain magnifying glass, it produces an angular magnification of 7.0 with the image very distant. What is the focal length of the lens of this Magnifying glass?

Astronomers are proud of their telescopes and often say they can "resolve a dime at so many miles." How many miles from a 102-cm-diameter telescope mirror can you place a coin of Diameter 3.0 cm and just resolve the coin using light of wavelength 389 nm? (1 mi = 1.609 km)

Mary builds a simple refracting telescope using two lenses of focal length 80 cm and 5.0 cm. The respective diameters are 60 mm and 10 mm. How many degrees wide does the moon appear through the telescope if it appears only 1/2 degree wide with the "naked eye"?

The near point of a farsighted person is 100 cm. She places reading glasses very close to her eyes, and with them she can comfortably read a book at a distance of 25 cm. What is the power of the Lenses in her reading glasses?

The objective lens and the eyepiece of a microscope have focal lengths of 4.0 mm and 25 mm, respectively. The objective produces a real image 30 times the size of the object, with the final Image viewed at infinity. The near point of the microscope user is at 25 cm. What is the distance Between the object and the focal point of the objective lens?

To maximize the magnification of a refracting telescope, what lenses should you choose?

A refracting telescope has a magnification M. If the focal length of the objective lens is doubled and the eyepiece focal length is halved, what is the new magnification?