Exam 25: Optical Instruments

Vicki very closely examines her new ruby ring with the jeweler's "loop." The ruby appears 7.0 times larger through this lens than when she views it close-up without the "loop." If her near point Is 35 cm, what is the focal length of the lens of the "loop"?

A farsighted person cannot see clearly objects that are closer to her eyes than 60.0 cm. Which one of the following combinations represents the correct focal length and the refractive power of the Contact lenses that will enable her to comfortably see the objects at a distance of 25.0 cm from her Eyes?

Alice is farsighted and cannot see objects clearly that are closer to her eye than 80.0 cm. What is the refractive power of the contact lenses that will enable her to comfortably see objects at a distance of 25)0 cm from her eyes?

Treat the pupil of your eye as a circular aperture of diameter 3.5 mm. Light of wavelength 500 nm is used to view two point sources that are 283 m distant from you. How far apart must these two point sources be if they are to be just barely resolved by your eye, assuming that the resolution is limited by diffraction?

The lattice spacing of the principal Bragg planes in sodium chloride is $0.282 \mathrm {~nm}$ . For what wavelength of x-rays will the first order reflected beam diffract at $55 ^ { \circ }$ with respect to the normal to the crystal planes?

The focal length of a camera lens is 40 mm and its aperture diameter is 10 mm. What is the f-number of this lens?

A nearsighted person has a far point that is 4.2 m from his eyes. What focal length lenses must he use in his contact lenses to allow him to focus on very distant mountains?

The objective lens of a telescope has a focal length of 1.90 m. When viewed through this telescope, the Moon appears 5.25 times larger than normal. How far apart are the objective lens and the eyepiece when this instrument is focused on the Moon?

A refracting telescope has an eyepiece of focal length -80 mm and an objective of focal length 36 cm. What is the magnification of this instrument?

Assuming a pupil diameter of 3 mm, what is the angular resolution of the human eye for light at the middle of the visible spectrum (550 nm)?

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.

A farsighted boy has a near point at 2.3 m and requires contact lenses to correct his vision to the normal near point. What is the correct choice of lens power for the contact lenses?

The angular magnification of a refracting telescope is 40. When the object and final image are both at infinity, the distance between the eyepiece and the objective is 143.5 cm. The telescope is used to View a distant radio tower. The real image of the tower, formed by the objective, is 6.0 mm in Height. The focal point of the eyepiece is positioned at the real image. What is the angle subtended By the final image of the tower?

The focal length of the lens of a simple digital camera is 40 mm, and it is originally focused on a person 25 m away. In what direction must the lens be moved to change the focus of the camera to A person 4.0 m away?

A person with a near point of 25 cm uses a magnifying lens having a focal length of 10 cm. What is the angular magnification of this lens if the person's eyes are focused at his near point?

A person with normal eyesight uses a converging lens of focal length $10 \mathrm {~cm}$ as a magnifying glass to finish an engraving job. To see detail, he holds the lens very close to his eyes. At what minimum distance from the job must he hold the lens?

You have available lenses of focal lengths 2.0 cm, 4.0 cm, 8.0 cm, and 16 cm. If you could use any two of these lenses to build a telescope, what is the lens separation for the telescope to provide the Maximum magnification for comfortable viewing of a planet?

A person cannot see clearly objects more than 70.0 cm away. What power of corrective lens should be prescribed if the glass is to be worn 1.00 cm in front of the eye?

Olga is nearsighted and cannot see things beyond 90 cm cm from her eyes. What is the refractive power of the contact lenses that will enable her to comfortably see distant buildings clearly?

A lens of focal length $45 \mathrm {~mm}$ is mounted on a $35 - \mathrm { mm }$ camera. The lens aperture is set at $f / 2.0$ and the shutter speed set at $1 / 2000 \mathrm {~s}$ . The photographer wants to keep the same exposure (amount of light), but wants to change the $f$ -number to $f / 8.0$ for greater depth of field. What should be the new shutter speed to maintain the same exposure?