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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

80 through 87 80, 87 SSM WWW 83 Two-lens systems. In Fig. 34-45, stick figure O (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 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 O or non-inverted (NI), and (e) on the same side of lens 2 as the object O or on the opposite side.

An object is placed against the center of a spherical mirror, and then moved70cmfrom it along the central axis as theimage distance i is measured. Figure 34-36 givesiversus object distancepout tops=40cm. What isifor p=70cm?

In Fig. 34-38, a beam of parallel light rays from a laser is incident on a solid transparent sphere of an index of refraction n. (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere? (b) What index of refraction, if any, will produce a point image at the center of the sphere?

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 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.)

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