33. Geometric Optics

A plano-concave glass lens (flat on one side, concave on the other) creates an with magnification +0.40 of an object 75 cm from the lens. What is the radius of curvature of the lens's curved surface?

High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun's light to a small spot that can burn things. As an engineer, you have designed a laser cutting device in which the material to be cut is placed 5.0 cm behind the lens. You have selected a high-power laser with a wavelength of 1.06 μm. Your calculations indicate that the laser must be focused to a 5.0-μm-diameter spot in order to have sufficient power to make the cut. What is the minimum diameter of the lens you must install?

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

You want to design a spy satellite to photograph license plate numbers. Assuming it is necessary to resolve points separated by 2 cm with 550-nm light, and that the satellite orbits at a height of 130 km, what minimum lens aperture (diameter) is required?

The lens shown in FIGURE CP35.49 is called an achromatic doublet, meaning that it has no chromatic aberration. The left side is flat, and all other surfaces have radii of curvature R. Because of dispersion, either lens alone would focus red rays and blue rays at different points. Define ∆n₁ and ∆n₂ as n_blue - n_red for the two lenses. What value of the ratio ∆n₁ / ∆n₂ makes f_blue = f_red for the two-lens system? That is, the two-lens system does not exhibit chromatic aberration.

A converging lens with focal length of 13.0 cm is placed in contact with a diverging lens with a focal length of -18.0 cm. What is the focal length of the combination, and is the combination converging or diverging?

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? (c) Where is the final image? Compare your answer to Fig. 34.43a.

An object is 60 cm from a screen. What are the radii of a symmetric converging plastic lens (i.e., two equally curved surfaces) that will form an image on the screen twice the height of the object?

Students in a physics lab are assigned to find the location where a bright object may be placed in order that a converging lens with ƒ = 12 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.

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?

Some electro-optic materials can change their index of refraction in response to an applied voltage. Suppose a plano-convex lens (flat on one side, a 15.0 cm radius of curvature on the other), made from a material whose normal index of refraction is 1.500, is creating an image of an object that is 50.0 cm from the lens. By how much would the index of refraction need to be increased to move the image 5.0 cm closer to the lens?

A 15-cm-focal-length converging lens is 20 cm to the right of a 7.0-cm-focal-length converging lens. A 1.0-cm-tall object is distance L to the left of the 7.0-cm-focal-length lens. What are the height and orientation of the final image?

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 image are at infinity. Find the height of the image formed by the objective of a building 60.0 m tall, 3.00 km away.

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

A fortune teller's 'crystal ball' (actually just glass) is 10 cm in diameter. Her secret ring is placed 6.0 cm from the edge of the ball. The crystal ball is removed and a thin lens is placed where the center of the ball had been. If the image is still in the same position, what is the focal length of the lens?