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Chapter 34: Q138P (page 1046)

A grasshopper hops to a point on the central axis of a spherical mirror. The absolute magnitude of the mirror’s focal length is 40.0cm, and the lateral magnification of the image produced by the mirror is +0.200. (a) Is the mirror convex or concave? (b) How far from the mirror is the grasshopper?

Short Answer

Expert verified
  1. It is a convex mirror.
  2. Object distance, p=160cm

Step by step solution

01

Determine the given quantities

The magnitude of focal length, f=40.0cm

Lateral magnification, m=+0.2

02

Determine the concepts of magnification

Using the formula for lateral magnification, we can find out the sign of image distance. If it is negative, then one can guess the sign of the focal length. Using the mirror formula, object distance can be calculated.

Formula:

Mirror’s formula1p+1i=1f

Lateral magnificationm=-ip

03

(a) Calculate the type of the lens

Consider the lateral magnification as

m=-ip=+0.2

Therefore, i=-0.2×p, i<0,and the image is diminished in size, which implies that the spherical mirror has f=-40.0cm.

Therefore, it is a convex mirror.

04

(b) Calculate the object distance

Consider the mirror’s formula:

1p+1i=1f

Substituteiandfin the above equation and solve as:

1p-102p=-140

22p-102p=-140

2-102p=-140

p=160cm

Object distance,p=160cm

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Most popular questions from this chapter

A moth at about eye level is10 cmin front of a plane mirror; a man is behind the moth,30 cmfrom the mirror. What is the distance between man’s eyes and the apparent position of the moth’s image in the mirror?

(a) Show that if the object O in Fig. 34-19c is moved from focal point F1toward the observer’s eye, the image moves in from infinity and the angle (and thus the angular magnification mu) increases. (b) If you continue this process, where is the image when mu has its maximum usable value? (You can then still increase, but the image will no longer be clear.) (c) Show that the maximum usable value of ismθ=1+25cmf.(d) Show that in this situation the angular magnification is equal to the lateral magnification.

80 through 87 80, 87 SSM WWW 83 Two-lens systems. In Fig. 34-45, stick figure (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to, which is at object distance p1. Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lenses and different values for distances, which are given in centimeters. The type of lens is indicated by converging and for diverging; the number after or is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2for the image produced by lens 2 (the final image produced by the system) and (b) the overall lateral magnification Mfor the system, including signs. Also, determine whether the final image is (c) real (R)or virtual (V), (d) inverted(I) from object or non-inverted (NI), and (e) on the same side of lens 2 as the object or on the opposite side.

9, 11, 13 Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance ps(centimeters), the type of mirror, and then the distance (centimeters, without proper sign) between the focal point and the mirror. Find (a) the radius of curvature r(including sign), (b) the image distance localid="1662986561416" i, and (c) the lateral magnification m. Also, determine whether the image is (d) real (R) or virtual (V), (e) inverted (I) from object O or non-inverted (NI), and (f) on the same side of the mirror as O or on the opposite side.

9, 11, 13 Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance ps(centimeter), the type of mirror, and then the distance (centimeters, without proper sign) between the focal point and the mirror. Find (a) the radius of curvature(including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real(R)or virtual (V), (e) inverted from object O or non-inverted localid="1663055514084" (NI), and (f) on the same side of the mirror as O or on the opposite side.
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