33. Geometric Optics

Repeat Exercise 34.41 using the same lenses except for the following changes: The second lens is a diverging lens having a focal length of magnitude 60.0 cm.

It is desired to magnify reading material by a factor of 3.0 x when a book is placed 9.0 cm behind a lens.

(a) Draw a ray diagram and describe the type of image this would be.

(b) What type of lens is needed?

(c) What is the power of the lens in diopters?

(II) Two lenses, one converging with focal length 20.0 cm and one diverging with focal length -10.0 cm, are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine (a) the position and (b) the magnification of the final image formed. (c) Sketch a ray diagram for this system.

Two converging lenses, one with ƒ = 4.0 cm and the other with ƒ = 41 cm , are made into a telescope. (a) Determine the telescope’s length and its magnification. Which lens should be the eyepiece? (b) Assume these lenses are now combined to make a microscope; if the magnification needs to be 125 x , how long would the microscope be? Explain why the result in (b) is so impractical.

Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apart. An object is placed 35.0 cm in front of one lens.

(a) Where will the final image formed by the second lens be located?

(b) What is the total magnification?

A 1.0-cm-tall object is 60 cm in front of a diverging lens that has a −30 cm focal length. Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.

An object is 20 cm in front of a converging lens with a focal length of 10 cm. Use ray tracing to determine the location of the image. Is the upright or inverted?

A 105-mm-focal-length lens is used to focus an image on the sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 132 mm.

(a) How far in front of the sensor should the lens (assumed thin) be positioned if the object to be photographed is 10.0 m away? (b) 3.0 m away? (c) 1.0 m away?

(d) What is the closest object this lens could photograph sharply?

A 1.20 cm tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0 cm.

(I) (a) What is the power of a 26.5-cm-focal-length lens? (b) What is the focal length of a -6.25 -D lens? Are these lenses converging or diverging?

A small object is 25.0 cm from a diverging lens as shown in Fig. 33–48. A converging lens with a focal length of 12.0 cm is 30.0 cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens. What is the focal length of the diverging lens?

A sharp image is located 373 mm behind a 235-mm-focal-length converging lens. Find the object distance by calculation.

Both a converging lens and a concave mirror can produce virtual images that are larger than the object. Concave mirrors can be used as magnifying makeup or shaving mirrors, but converging lenses cannot be. (a) Draw ray diagrams to explain why not. (b) If a concave mirror has the same focal length as a converging lens, and an object is placed first at a distance of (1/2)ƒ from the lens and then at a distance of (1/2)ƒ from the mirror, how will the magnification of the object compare in the two cases?

An object is 16.0 cm to the left of a lens. The lens forms an image 36.0 cm to the right of the lens. Draw a principal-ray diagram.