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Chapter 34: Q121P (page 1045)

An object is 20cmto the left of a thin diverging lens that has a 30cmfocal length. (a) What is the image distance i? (b) Draw a ray diagram showing the image position.

Short Answer

Expert verified
  1. The image distance i is -12cm.
  2. The ray diagram is drawn showing the image position.

Step by step solution

01

Listing the given quantities

Object distance p=20cm

Focal length of the lens f = -30cm

02

Understanding the concepts of lens equation

Here, we need to use the equation of a lens to calculate the image distance for a diverging lens.

We can draw a ray diagram showing the image position using two rays, the ray passing through the center of lens and other ray passing parallel to the principle axis.

Formula:

1p+1i=1f

03

Calculations of the image distance

(a)

The lens equation relates an object distance p, lens focal length f and the image distance i as

1p+1i=1f1i=1f-1p1i=p-ffpi=pfp-f=(20cm)(-30cm)(20cm--30cm)=-12cm

The negative sign shows that the image isvirtualand to the left side of the lens.

The image distance i is -12cm.

04

Step 4: The ray diagram showing the image position

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Most popular questions from this chapter

An object is placed against the center of a thin lens and then moved 70 cm from it along the central axis as the image distance is measured. Figure 34-42 gives i versus object distance p out to ps = 40 cm. What is the image distance when p=70 cm ?

An object is placed against the center of a spherical mirror and then moved 70 cm from it along the central axis as the image distance i is measured. Figure 34-48 gives i versus object distance p out to ps=40cm. What is the image distance when the object is 70 cm from the mirror?

In Fig. 34-51, a box is somewhere at the left, on the central axis of the thin converging lens. The image Imof the box produced by the plane mirror is 4.00cm 鈥渋nside鈥� the mirror. The lens鈥搈irror separation is 10.0cm, and the focal length of the lens is 2.00cm. (a) What is the distance between the box and the lens? Light reflected by the mirror travels back through the lens, which produces a final image of the box. (b) What is the distance between the lens and that final image?

In Fig. 34-54, a fish watcher at point P watches a fish through a glass wall of a fish tank. The watcher is level with the fish; the index of refraction of the glass is 8/5, and that of the water is 4/3. The distances are d1=8.0cm,d2=3.0cm,d3=6.8cm. (a) To the fish, how far away does the watcher appear to be? (Hint: The watcher is the object. Light from that object passes through the walls outside surface, which acts as a refracting surface. Find the image produced by that surface. Then treat that image as an object whose light passes through the walls inside surface, which acts as another refracting surface.) (b) To the watcher, how far away does the fish appear to be?

In a microscope of the type shown in Fig. 34-20, the focal length of the objective is 4.00 cm, and that of the eyepiece is 8.00 cm. The distance between the lenses is 25.00 cm. (a) What is the tube length s? (b) If image I in Fig. 34-20 is to be just inside focal point F1, how far from the objective should the object be? What then are (c) the lateral magnification m of the objective, (d) the angular magnification m胃 of the eyepiece, and (e) the overall magnification M of the microscope?
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