33. Geometric Optics

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 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?

(II) A diverging lens with ƒ = -36.5 cm is placed 14.0 cm behind a converging lens with ƒ = 20.0cm . Where will an object at infinity be focused?

A physicist lost in the mountains tries to make a telescope using the lenses from his reading glasses. They have powers of +2.0 D and +4.5 D, respectively. (a) What maximum magnification telescope is possible? (b) Which lens should be used as the eyepiece?

(I) 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?

(II) 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?

(II) A stamp collector uses a converging lens with focal length 28 cm to view a stamp 15 cm in front of the lens. (a) Where is the image located? (b) What is the magnification?

(II) How far from a converging lens with a focal length of 25 cm should an object be placed to produce a real image which is the same size as the object?

(II) How far apart are an object and an image formed by a 78-cm-focal-length converging lens if the image is 2.95 x larger than the object and is real?

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?

(II) An object is located 1.35 m from an 8.0-D lens. By how much does the image move if the object is moved (a) 0.90 m closer to the lens, and (b) 0.90 m farther from the lens?

(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 ?

(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 = dᵢ + dₒ between the object and the screen is kept fixed, but the lens can be moved.

(a) Show that if d_T > 4ƒ, there will be two positions where the lens can be placed and a sharp image will be produced on the screen.

(b) If d_T < 4ƒ, show that there will be no lens position where a sharp image is formed.

(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

(II) 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?

(II) A symmetric double convex lens with a focal length of 20.5 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surface?

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?

A movie star catches a reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.55 mm high on the film, and the focal length of the camera lens was 220 mm. How far away from the subject was the reporter standing?

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

(II) How many uncoated thin lenses in an optical instrument would reduce the amount of light passing through the instrument to 50% or less? (Assume the same transmission percent at each of the two surfaces—see page 1008.)

II) 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.]

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)?

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.

(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 = dᵢ + dₒ between the object and the screen is kept fixed, but the lens can be moved.

(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.