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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

An object is placed against the center of a thin lens and then moved away from it along the central axis as the image distance is measured. Figure 34-41 gives i versus object distance p out to ps=60cm. What is the image distancewhen p=100cm?

An object is moved along the central axis of a spherical mirror while the lateral magnification m of it is measured. Figure 34-35 gives m versus object distance p for the rangepa=2cm and pb=8.0cm. What is m for p=14cm?

Suppose the farthest distance a person can see without visual aid is50cm. (a) What is the focal length of the corrective lens that will allow the person to see very far away? (b) Is the lens converging or diverging? (c) The power Pof a lens (in diopters) is equal to1/f, wherefis in meters. What ispfor the lens?

A simple magnifier of focal length fis placed near the eye of someone whose near point Pn is25 cm . An object is positioned so that its image in the magnifier appears atPn. (a) What is the angular magnification of the magnifier? (b) What is the angular magnification if the object is moved so that its image appears at infinity? For f=10 cm, evaluate the angular magnifications of (c) the situation in (a) and (d) the situation in (b). (Viewing an image atPnrequires effort by muscles in the eye, whereas viewing an image at infinity requires no such effort for many people.)

A narrow beam of parallel light rays is incident on a glass sphere from the left, directed toward the center of the sphere. (The sphere is a lens but certainly not a thin lens.) Approximate the angle of incidence of the rays as 0°, and assume that the index of refraction of the glass is n<2.0(a) In terms of n and the sphere radius r, what is the distance between the image produced by the sphere and the right side of the sphere? (b) Is the image to the left or right of that side? (Hint: Apply Eq. 34-8 to locate the image that is produced by refraction at the left side of the sphere; then use that image as the object for refraction at the right side of the sphere to locate the final image. In the second refraction, is the object distance positive or negative?)
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