Chapter 35: Optical Instruments

A $1.0cm$-tall object is $110cm$from a screen. A diverging lens with focal length$-20cm$is $20cm$in front of the object. What are the focal length and distance from the screen of a second lens that will produce a well-focused, $2.0cm$-tall image on the screen?

A $15cm$-focal-length converging lens is $20cm$to the right of a $7.0cm$-focal-length converging lens. A $1.0cm$-tall object is distance L to the left of the first lens.

a. For what value of L is the final image of this two-lens system halfway between the two lenses?

b. What are the height and orientation of the final image?

Yang can focus on objects $150cm$ away with a relaxed eye. With full accommodation, she can focus on objects $20cm$away. After her eyesight is corrected for distance vision, what will her near point be while wearing her glasses?

The cornea, a boundary between the air and the aqueous humor, has a $3.0cm$focal length when acting alone. What is its radius of curvature?

The objective lens of a telescope is a symmetric glass lens with $100cm$radii of curvature. The eyepiece lens is also a symmetric glass lens. What are the radii of curvature of the eyepiece lens if the telescope’s magnification is $20\times$?

Mars $(6800kmdiameter)$is viewed through a telescope on a night when it is $1.1\times {10}^{8}km$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 $25mm$, how long is the telescope?

You’ve been asked to build a telescope from a $2.0x$magnifying lens and a $5.0x$magnifying lens.

a. What is the maximum magnification you can achieve?

b. Which lens should be used as the objective? Explain.

c. What will be the length of your telescope?

| 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. a. Which lens should you use for the objective and which for the eyepiece? Explain.

b. What will be the magnification of your telescope?

c. How far apart should the two lenses be when you focus on distant objects?

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 $+4.5D$and your right eye’s lens is $+3.0D$. a. Which lens should you use for the objective and which for the eyepiece? Explain.

b. What will be the magnification of your telescope?

c. How far apart should the two lenses be when you focus on distant objects?

A microscope with a tube length of 180 mm achieves a total magnification of 800* with a 40* objective and a 20* eyepiece. The microscope is focused for viewing with a relaxed eye. How far is the sample from the objective lens?