33. Geometric Optics

A thin lens with a focal length of 6.00 cm is used as a simple magnifier. (a) What angular magnification is obtainable with the lens if the object is at the focal point?

BIO A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. (c) What focal length contact lens is needed, and what is its power in diopters?

BIO A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. (a) Is she nearsighted or farsighted?

BIO Ordinary Glasses. Ordinary glasses are worn in front of the eye and usually 2.0 cm in front of the eyeball. Suppose that the person in Exercise 34.52 prefers ordinary glasses to contact lenses. What focal length lenses are needed to correct his vision, and what is their power in diopters?

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

A telescope is constructed from two lenses with focal lengths of 95.0 cm and 15.0 cm, the 95.0-cm lens being used as the objective. Both the object being viewed and the final are at infinity. (b) Find the height of the formed by the objective of a building 60.0 m tall, 3.00 km away.

Resolution of a Microscope. The formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. The eyepiece has a focal length of 26.0 mm. (a) What is the angular magnification of the microscope?

The focal length of the eyepiece of a certain microscope is 18.0 mm. The focal length of the objective is 8.00 mm. The distance between objective and eyepiece is 19.7 cm. The final formed by the eyepiece is at infinity. Treat all lenses as thin. (b) What is the magnitude of the linear magnification produced by the objective?

The focal length of a simple magnifier is 8.00 cm. Assume the magnifier is a thin lens placed very close to the eye. (b) If the object is 1.00 mm high, what is the height of its formed by the magnifier?

BIO Contact Lenses. Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or ) is the same as the distance from the lens to that object (or ). A certain person can see distant objects well, but his near point is 45.0 cm from his eyes instead of the usual 25.0 cm. (a) Is this person nearsighted or farsighted?

A lightbulb is 3.0 m from a wall. What are the focal length and the position (measured from the bulb) of a lens that will form an on the wall that is twice the size of the lightbulb?

A lens forms an of an object. The object is 16.0 cm from the lens. The is 12.0 cm from the lens on the same side as the object. (a) What is the focal length of the lens? Is the lens converging or diverging?

A converging lens with a focal length of 70.0 cm forms an of a 3.20-cm-tall real object that is to the left of the lens. The is 4.50 cm tall and inverted. Where are the object and located in relation to the lens? Is the real or virtual?

A converging lens with a focal length of 9.00 cm forms an of a 4.00-mm-tall real object that is to the left of the lens. The is 1.30 cm tall and erect. Where are the object and located? Is the real or virtual?

A lensmaker wants to make a magnifying glass from glass that has an index of refraction n = 1.55 and a focal length of 20.0 cm. If the two surfaces of the lens are to have equal radii, what should that radius be?

For each thin lens shown in Fig. E34.37, calculate the location of the of an object that is 18.0 cm to the left of the lens. The lens material has a refractive index of 1.50, and the radii of curvature shown are only the magnitudes. (b)

An object is 16.0 cm to the left of a lens. The lens forms an 36.0 cm to the right of the lens. (b) If the object is 8.00 mm tall, how tall is the ? Is it erect or inverted?

You wish to project the of a slide on a screen 9.00 m from the lens of a slide projector. (b) If the dimensions of the picture on a 35-mm color slide are 24 mm * 36 mm, what is the minimum size of the projector screen required to accommodate the ?

Zoom Lens. Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f1 = 12 cm, and the diverging lens has focal length f2 = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. (a) For a distant object, where is the of the converging lens? (b) The of the converging lens serves as the object for the diverging lens. What is the object distance for the diverging lens? (c) Where is the final ? Compare your answer to Fig. 34.43a.

A camera lens has a focal length of 180.0 mm and an aperture diameter of 16.36 mm. (a) What is the ƒ-number of the lens?

A 25-cm-long rod lies along the optical axis of a converging lens, perpendicular to the lens plane. The lens has a 30 cm focal length. The rod's real , along the optical axis on the other side of the lens, is also 25 cm long. What is the distance from the lens to the nearest end of the rod?

FIGURE CP35.50 shows a lens combination in which the lens separation is less than the focal length of the converging lens. The procedure for combination lenses is to let the of the first lens be the object for the second lens, but in this case the of the first lens—shown as a dot—is on the far side of the second lens. This is called a virtual object, a point that light rays are converging toward but never reach. The top half of Figure CP35.50 shows that the converging rays are refracted again by the diverging lens and come to a focus farther to the right. The procedure for combination lenses will continue to work if we use a negative object distance for a virtual object. b. Equation 35.1 defined the effective focal length fₑբբ of a lens combination, but we didn't discuss how it is used. Although an actual ray refracts twice, once at each lens, we can extend the output rays leftward to where they need to bend only once in a plane called the principal plane. The principal plane is similar to the lens plane of a single lens, where a single bend occurs, but the principal plane generally does not coincide with the physical lens; it's just a mathematical plane in space. The effective focal length is measured from the principal plane, so parallel input rays are focused at distance fₑբբ beyond the principal plane. Find the positions of the principal planes for lens separations of 5 cm and 10 cm. Give your answers as distances to the left of the diverging lens.