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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

The formula 1p+1i=1f is called the Gaussian form of the thin-lens formula. Another form of this formula, the Newtonian form, is obtained by considering the distance xfrom the object to the first focal point and the distancex' from the second focal point to the image. Show thatxx'=f2 is the Newtonian form of the thin-lens formula

Figure 34-33 shows an overhead view of a corridor with a plane mirror Mmounted at one end. A burglar Bsneaks along the corridor directly toward the center of the mirror. Ifd=3m, how far from the mirror will she from the mirror when the security guardScan first see her in the mirror?

58 through 67 61 59 Lenses with given radii. An object Ostands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance O, index of refraction n of the lens, radius of the nearer lens surface, and radius of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real or virtual , (d) inverted from the object Oor non-inverted , and (e) on the same side of the lens as object or on the opposite side.

32 through 38 37, 38 33, 35 Spherical refracting surfaces. An object Ostandson the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refractionn1where the objectis located, (a) the index of refraction n2on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature rof the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R)or virtual (V)and (f) on the same side of the surface asthe object Oor on the opposite side.

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 O, 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 C for converging and D for diverging; the number after C or D 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 localid="1663045000066" 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 localid="1663045476655" (V), (d) inverted (I)from object O or non-inverted (NI), and (e) on the same side of lens 2 as object O or on the opposite side.
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