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Chapter 24: Problem 17

A photographer wishes to take a photograph of the Eiffel Tower $(300 \mathrm{m}\( tall ) from across the Seine River, a distance of \)300 \mathrm{m}$ from the tower. What focal length lens should she use to get an image that is 20 mm high on the film?

Short Answer

Expert verified
Answer: The photographer should use a lens with a focal length of approximately 19.96 mm.

Step by step solution

01

Write down the given information

The height of the Eiffel Tower is 300 m, the distance from the photographer to the Tower (object distance) is 300 m, and we need an image 20 mm high on the film. We must find the focal length of the lens.
02

Determine the object distance (d_o) and image distance (d_i)

The object distance (d_o) is the distance from the lens to the object, which is 300 m.
03

Determine the magnification formula

The magnification formula is: magnification = (image height) / (object height) = (-d_i) / (d_o)
04

Solve for the image height

The image height is given as 20 mm. Since we're dealing with distances in meters, let's convert the image height to meters: 20 mm = 0.02 m.
05

Calculate the magnification

Now we will calculate the magnification using the formula. magnification = (0.02 m) / (300 m) = 1 / 15000
06

Determine the thin lens formula

The thin lens formula is: 1 / f = 1 / d_o + 1 / d_i
07

Use magnification and thin lens formulas to solve for f

Since magnification = (-d_i) / (d_o), we can rewrite this equation in terms of d_i: d_i = -d_o * magnification Now plug in the values for d_o and magnification: d_i = -300 m * (1 / 15000) = -0.02 m The image will be 0.02 m behind the lens. Now, use the thin lens formula to find the focal length: 1 / f = (1 / 300) + (1 / (-0.02))
08

Solve for the focal length

We will now solve for the focal length, f: 1 / f = (1 / 300) - (1 / 0.02) f = 1 / ((1 / 300) - (1 / 0.02)) f ≈ 0.01996 m or 19.96 mm The photographer should use a lens with a focal length of approximately 19.96 mm to get an image of the Eiffel Tower that is 20 mm high on the film.

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Most popular questions from this chapter

A statue is \(6.6 \mathrm{m}\) from the opening of a pinhole camera, and the screen is \(2.8 \mathrm{m}\) from the pinhole. (a) Is the image erect or inverted? (b) What is the magnification of the image? (c) To get a brighter image, we enlarge the pinhole to let more light through, but then the image looks blurry. Why? (d) To admit more light and still have a sharp image, we replace the pinhole with a lens. Should it be a converging or diverging lens? Why? (e) What should the focal length of the lens be?
(a) What is the angular size of the Moon as viewed from Earth's surface? See the inside back cover for necessary information. (b) The objective and eyepiece of a refracting telescope have focal lengths \(80 \mathrm{cm}\) and \(2.0 \mathrm{cm}\) respectively. What is the angular size of the Moon as viewed through this telescope?
A converging lens with a focal length of \(3.00 \mathrm{cm}\) is placed $24.00 \mathrm{cm}\( to the right of a concave mirror with a focal length of \)4.00 \mathrm{cm} .\( An object is placed between the mirror and the lens, \)6.00 \mathrm{cm}\( to the right of the mirror and \)18.00 \mathrm{cm}$ to the left of the lens. Name three places where you could find an image of this object. For each image tell whether it is inverted or upright and give the total magnification.
The distance from the lens system (cornea + lens) of a particular eye to the retina is \(1.75 \mathrm{cm} .\) What is the focal length of the lens system when the eye produces a clear image of an object \(25.0 \mathrm{cm}\) away?
Veronique is nearsighted; she cannot sce clearly anything more than $6.00 \mathrm{m}$ away without her contacts. One day she doesn't wear her contacts; rather, she wears an old pair of glasses prescribed when she could see clearly up to \(8.00 \mathrm{m}\) away. Assume the glasses are \(2.0 \mathrm{cm}\) from her eyes. What is the greatest distance an object can be placed so that she can see it clearly with these glasses?
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