33. Geometric Optics

A 2.0-cm-tall object is 15 cm in front of a plano-convex polystyrene plastic lens that has a 13 cm radius of curvature. What are the (a) position and (b) height of the image?

Where is the near point of an eye for which a contact lens with a power of +2.75 diopters is prescribed?

An object is placed so it is touching one surface of a thin lens. Where is the image in this case (i.e., when dₒ approaches 0)?

Find the focal length of the plano-concave polystyrene plastic lens in FIGURE EX34.25.

Two converging lenses are placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?

An object is placed 96.0 cm from a glass lens (n = 1.52) with one concave surface of radius 22.0 cm and one convex surface of radius 18.5 cm.

(a) Where is the final image?

(b) What is the magnification?

An old-fashioned slide projector needs to create a 98-cm-high of a 2.0-cm-tall slide. The screen is 300 cm from the slide. What focal length does the lens need? Assume that it is a thin lens.

A bright object and a viewing screen are separated by a distance of 86.0 cm. At what location(s) between the object and the screen should a lens of focal length 16.0 cm be placed in order to produce a sharp image on the screen? [Hint: First draw a diagram.]

What is the power of a lens with a focal length of 25 mm?

A 1.0-cm-tall object is 110 cm from a screen. A diverging lens with focal length -20 cm is 20 cm 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, 2.0-cm-tall on the screen?

Sunlight is observed to focus at a point 16.5 cm behind a lens. (a) What kind of lens is it? (b) What is its power in diopters?

BIO The Lens of the Eye. The crystalline lens of the human eye is a double-convex lens made of material having an index of refraction of 1.44 (although this varies). Its focal length in air is about 8.0 mm, which also varies. We shall assume that the radii of curvature of its two surfaces have the same magnitude. Find the radii of curvature of this lens.

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

(II) A planoconvex lens (Fig. 33–2a) has one flat surface and the other has R = 15.3 cm. This lens is used to view a red and yellow object which is 62.0 cm away from the lens. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens?

A certain lens focuses an object 2.15 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?