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Chapter 24: Problem 56

A camera has a telephoto lens of 240 -mm focal length. The lens can be moved in and out a distance of \(16 \mathrm{mm}\) from the film plane by rotating the lens barrel. If the lens can focus objects at infinity, what is the closest object distance that can be focused?

Short Answer

Expert verified
Answer: The closest object distance that can be focused with these specifications is approximately 3360mm.

Step by step solution

01

Find the Image Distance when focusing on the closest object

When the lens is moved inwards by 16mm, the distance from the film plane is reduced, meaning the image distance is now 240mm - 16mm: \(d_i = 240\mathrm{mm} - 16\mathrm{mm} = 224\mathrm{mm}\) With this new value for \(d_i\), we can calculate the closest object distance.
02

Use the Thin Lens Equation to Calculate the Closest Object Distance

Using the thin lens equation, \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\), and the values for \(f\) and \(d_i\) from the previous step, we can find the closest object distance \(d_o\). Substituting the values, we get: \(\frac{1}{240\mathrm{mm}} = \frac{1}{d_o} + \frac{1}{224\mathrm{mm}}\) Now, we need to solve for \(d_o\).
03

Solve for Closest Object Distance

To solve for \(d_o\), first subtract \(\frac{1}{224\mathrm{mm}}\) from both sides: \(\frac{1}{240\mathrm{mm}} - \frac{1}{224\mathrm{mm}} = \frac{1}{d_o}\) Now, find a common denominator: \(\frac{224 - 240}{240 \times 224} = \frac{1}{d_o}\) Simplifying the fraction: \(\frac{-16}{240 \times 224} = \frac{1}{d_o}\) Now, take the reciprocal of the fractions: \(d_o = -\frac{240 \times 224}{16}\) Finally, since object distance is positive, we can remove the negative sign: \(d_o = \frac{240 \times 224}{16}\) Now, calculate the value for \(d_o\): \(d_o \approx 3360\mathrm{mm}\) The closest object distance that can be focused is approximately 3360mm.

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Most popular questions from this chapter

Esperanza uses a 35 -mm camera with a standard lens of focal length $50.0 \mathrm{mm}\( to take a photo of her son Carlos, who is \)1.2 \mathrm{m}$ tall and standing \(3.0 \mathrm{m}\) away. (a) What must be the distance between the lens and the film to get a properly focused picture? (b) What is the magnification of the image? (c) What is the height of the image of Carlos on the film?
A nearsighted man cannot clearly see objects more than \(2.0 \mathrm{m}\) away. The distance from the lens of the eye to the retina is \(2.0 \mathrm{cm},\) and the eye's power of accommodation is \(4.0 \mathrm{D}\) (the focal length of the cornea-lens system increases by a maximum of \(4.0 \mathrm{D}\) over its relaxed focal length when accommodating for nearby objects). (a) As an amateur optometrist, what corrective eyeglass lenses would you prescribe to enable him to clearly see distant objects? Assume the corrective lenses are $2.0 \mathrm{cm}$ from the eyes. (b) Find the nearest object he can see clearly with and without his glasses.
Angular Magnification and the Simple Magnifier Thomas wants to use his 5.5 -D reading glasses as a simple magnifier. What is the angular magnification of this lens when Thomas's eye is relaxed?
A camera uses a 200.0 -mm focal length telephoto lens to take pictures from a distance of infinity to as close as 2.0 \(\mathrm{m}\). What are the minimum and maximum distances from the lens to the film?
Keesha is looking at a beetle with a magnifying glass. She wants to see an upright, enlarged image at a distance of \(25 \mathrm{cm} .\) The focal length of the magnifying glass is \(+5.0 \mathrm{cm} .\) Assume that Keesha's eye is close to the magnifying glass. (a) What should be the distance between the magnifying glass and the beetle? (b) What is the angular magnification? (tutorial: magnifying glass II).
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