33. Geometric Optics

A scientist needs to focus a helium-neon laser beam (⋋ = 633 nm) to a 10-μm-diameter spot 8.0 cm behind a lens. What minimum diameter must the lens have?

(II) In a film projector, the film acts as the object whose image is projected on a screen (Fig. 33–46). If a 105-mm-focal-length lens is to project an image on a screen 22.5 m away, how far from the lens should the film be? If the film is 24 mm wide, how wide will the picture be on the screen?

Find the focal length of the glass lens in FIGURE EX34.28.

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. Is she nearsighted or farsighted?

An astronomical telescope, Fig. 33–36, produces an inverted image. One way to make a telescope that produces an upright image is to insert a third lens between the objective and the eyepiece, Fig. 33–39b. To have the same magnification, the non-inverting telescope will be longer. Suppose lenses of focal length 150 cm, 1.5 cm, and 10 cm are available. Where should these three lenses be placed to make a non-inverting telescope with magnification 100x?

(III) A bright object is placed on one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distance d_T = d_i + d_o between the object and the screen is kept fixed, but the lens can be moved. Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

For each thin lens shown in Fig. E34.37, calculate the location of the image 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.

A biconvex lens has a focal length of 12 cm. If an object is placed 5 cm from the lens, where is the image formed? Is it real or virtual? Is it upright or inverted? What's the height of the image if the object is 2 cm tall?

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?

An object is moving toward a converging lens of focal length ƒ with constant speed v_o, but its distance d_o from the lens is always greater than f. (a) Determine the velocity vᵢ of the image as a function of d_o. (b) Which direction (toward or away from the lens) does the image move? (c) For what d_o does the image’s speed equal the object’s speed?

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?

(II) (a) How far from a 75.0-mm-focal-length lens must an object be placed if its image is to be magnified 2.50 x and be real? (b) What if the image is to be virtual and magnified 2.50 x?

A camera’s close-up lens is aimed at a butterfly 200 mm in front of the lens, creating a focused on the detector 50 mm behind the lens. A proper exposure requires an f-number of F8.0. What is the correct diameter of the lens aperture?

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 image formed by the eyepiece is at infinity. Treat all lenses as thin. What is the magnitude of the linear magnification produced by the objective?

Two identical concave mirrors are set facing each other 1.0 m apart. A small lightbulb is placed halfway between the mirrors. A small piece of paper placed just to the left of the bulb prevents light from the bulb from directly shining on the left mirror, but light reflected from the right mirror still reaches the left mirror. A good image of the bulb appears on the left side of the piece of paper. What is the focal length of the mirrors?