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Chapter 34: Q90P (page 1042)

Figure 34-46a shows the basic structure of an old film camera. A lens can be moved forward or back to produce an image on film at the back of the camera. For a certain camera, with the distance i between the lens and the film set at f = 5.00 cm, parallel light rays from a very distant object O converge to a point image on the film, as shown. The object is now brought closer, to a distance of p = 100 cm, and the lens–film distance is adjusted so that an inverted real image forms on the film (Fig. 34-46b). (a) What is the lens–film distance i now? (b) By how much was distance i changed?

Short Answer

Expert verified
  1. The lens-film distanceis 5.3 cm.
  2. The change in lens-film distance i is 0.30 cm.

Step by step solution

01

Step 1: Given data

  • Focal length,f=5.0cm .
  • Object distance, p=100cm.
02

Determining the concept

Using the lens formula, calculate the lens-film distance, which is image distance i. Using this, the change in lens-film distance can be calculated.

Formulae are as follows:

1f=1p+1i

Here, p is the pole, and i is the image distance, f is the focal length.

03

(a) Determining the lens-film distance i

According to equation 34-4, find the image distance as,

1f=1p+1i

Rearranging this formula gives,

1i=1f-1p

So,

i=1f-1p-1

Substitute the values in the above expression, and we get,

i=15-1100-1=100×5100-5=50095=5.26cm

So,

i≈5.3cm

Therefore, the lens-film distance is 5.3 cm.

04

(b) Determine the change in lens-film distance i

The change in the lens-film distance:

Change in lens-film distance is,

Change=i-f=5.3-5.0=0.30cm

Therefore, the change in lens-film distance i is 0.30 cm.

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Most popular questions from this chapter

A pinhole camera has the hole a distance12cmfrom the film plane, which is a rectangle of height 8.0cmand width 6.0cm . How far from a painting of dimensions 50cm by 50cmshould the camera be placed so as to get the largest complete image possible on the film plane?

A concave shaving mirror has a radius of curvature of 35cm. It is positioned so that the (upright) image of a man’s face is 2.5 times the size of the face. How far is the mirror from the face?

17 through 29 22 23, 29 More mirrors. Object stands on the central axis of a spherical or plane mirror. For this situation, each problem in Table 34-4 refers to (a) the type of mirror, (b) the focal distance f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual(V), (h) inverted (I) or noninverted (NI)fromO, and (i) on the same side of the mirror as the object Oor the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

(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.

In Fig. 34-26, stick figure Ostands in front of a spherical mirrorthat is mounted within the boxed region;the central axis through themirror is shown. The four stick figures I1to I4suggest general locationsand orientations for the images that might be produced by themirror. (The figures are onlysketched in; neither their heightsnor their distances from the mirror are drawn to scale.) (a) Whichof the stick figures could not possibly represent images? Of thepossible images, (b) which would be due to a concave mirror, (c)which would be due to a convex mirror, (d) which would be virtual,and (e) which would involve negative magnification?
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