When the Object Is at 1.2 M, We Locate the Image From

Homework 13

Ch25: P 5, 15, 25, 27, 33, 43, 51

5. (II) If an telephoto lens is designed to cover object distances from 1.2 m to over what distance must the lens move relative to the plane of the film?

Solution

For an object at infinity, the image will be in the focal plane, so we have

When the object is at 1.2 m, we locate the image from

which gives

Thus the distance from the lens to the film must change by

15. (II) A person’s left eye is corrected by a lens, 2.0 cm from the eye. (a) Is this person’s left eye near- or farsighted? (b) What is this eye’s far point without glasses?

Solution

(a) Since the diopter is negative, the lens is diverging, so it produces images closer than the object; thus the person is nearsighted.

(b) We find the far point by finding the image distance for an object at infinity:

which gives

Because this is the distance from the lens, the far point without glasses is

25. (II) A 3.30-mm-wide beetle is viewed with a 9.50-cm-focal-length lens. A normal eye views the image at its near point. Calculate (a) the angular magnification, (b) the width of the image, and (c) the object distance from the lens.

Solution

(a) The angular magnification with the image at the near point is

(b) Because the object without the lens and the image with the lens are at the near point, the angular magnification is also the ratio of widths:

which gives

(c) We find the object distance from

which gives 6.88 cm from the lens.

27. (II) A magnifying glass with a focal length of 8.5 cm is used to read print placed at a distance of 7.5 cm. Calculate (a) the position of the image; (b) the angular magnification.

Solution

(a) We find the image distance from

which gives

(b) The angular magnification is

=

33. (II) An astronomical telescope has its two lenses spaced 75.2 cm apart. If the objective lens has a focal length of 74.5 cm, what is the magnification of this telescope? Assume a relaxed eye.

Solution

For both object and image far away, we find the focal length of the eyepiece from the

separation of the lenses:

which gives

The magnification of the telescope is given by

*43. (II) A microscope has a 1.8-cm-focal-length eyepiece and a 0.80-cm objective lens. Assuming a relaxed normal eye, calculate (a) the position of the object if the distance between the lenses is 16.0 cm, and (b) the total magnification.

Solution

(a) Because the image from the objective is at the focal point of the eyepiece, the image distance for the objective is

We find the object distance from the lens equation for the objective:

which gives

(b) With the final image at infinity, the magnification of the eyepiece is

The magnification of the objective is

.

The total magnification is

M=

51. (II) Two stars 15 light-years away are barely resolved by a 55-cm (mirror diameter) telescope. How far apart are the stars? Assume and that the resolution is limited by diffraction.

Solution

The resolution of the telescope is

The separation of the stars is