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

The lens-film distanceis 5.3 cm.
The change in lens-film distance i is 0.30 cm.

Step by step solution

Step 1: Given data

Focal length, $f = 5.0 cm$ .

Object distance, $p = 100 cm$ .

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:

$\frac{1}{f} = (\frac{1}{p} + \frac{1}{i})$

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

(a) Determining the lens-film distance i

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

$\frac{1}{f} = (\frac{1}{p} + \frac{1}{i})$

Rearranging this formula gives,

$\frac{1}{i} = \frac{1}{f} - \frac{1}{p}$

So,

$i = {(\frac{1}{f} - \frac{1}{p})}^{- 1}$

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

$\begin{array}{rcl} i & = & {(\frac{1}{5} - \frac{1}{100})}^{- 1} \\ = & \frac{100 \times 5}{100 - 5} \\ = & \frac{500}{95} \\ = & 5.26 cm \end{array}$

So,

$i \approx 5.3 cm$

Therefore, the lens-film distance is 5.3 cm.

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

The change in the lens-film distance:

Change in lens-film distance is,

$\begin{array}{rcl} Change & = & i - f \\ = & 5.3 - 5.0 \\ = & 0.30 cm \end{array}$

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

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Short Answer

Step by step solution

Step 1: Given data

Determining the concept

(a) Determining the lens-film distance i

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

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