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Chapter 24: Problem 11

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?

Short Answer

Expert verified
Answer: The minimum distance from the lens to the film is 222.22 mm and the maximum distance from the lens to the film is 200 mm.

Step by step solution

01

Identify the Thin Lens Equation

For this problem, we will use the Thin Lens Equation: 1/f = 1/u + 1/v Where f is the focal length of the lens, u is the object distance, and v is the image distance.
02

Plug in the given values of the focal length and object distance for minimum distance

We are given the focal length as f = 200 mm. For the minimum distance from the lens to the film, the object is at the closest possible distance, which is u = 2.0 m (or, 2,000 mm). We can now plug in these values into the Thin Lens Equation: 1/200 = 1/2000 + 1/v
03

Solve for the minimum distance from the lens to the film (v_min)

Rearrange the equation to get the value of v_min: 1/v_min = 1/200 - 1/2000 Now, to calculate v_min, you can take the inverse of the result: v_min = 1 / (1/200 - 1/2000) = 1 / (9/2000) = 222.22 mm So, the minimum distance from the lens to the film is 222.22 mm.
04

Plug in the given values of the focal length and object distance for maximum distance

For the maximum distance from the lens to the film, the object is at a distance of infinity so we can assume u is approaching infinity. Plug in the given values: 1/200 = 1/infinity + 1/v
05

Solve for the maximum distance from the lens to the film (v_max)

As the object distance (u) is approaching infinity, 1/u will approach 0. So the equation becomes: 1/200 = 0 + 1/v_max v_max = 200 mm So, the maximum distance from the lens to the film is 200 mm.
06

Conclude with the results

The minimum distance from the lens to the film is 222.22 mm and the maximum distance from the lens to the film is 200 mm.

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Most popular questions from this chapter

You have two lenses of focal length \(25.0 \mathrm{cm}\) (lens 1 ) and $5.0 \mathrm{cm}$ (lens 2 ). (a) To build an astronomical telescope that gives an angular magnification of \(5.0,\) how should you use the lenses (which for objective and which for eyepiece)? Explain. (b) How far apart should they be?
Two lenses, separated by a distance of \(21.0 \mathrm{cm},\) are used in combination. The first lens has a focal length of \(+30.0 \mathrm{cm} ;\) the second has a focal length of \(-15.0 \mathrm{cm} .\) An object, $2.0 \mathrm{mm}\( long, is placed \)1.8 \mathrm{cm}$ before the first lens. (a) What are the intermediate and final image distances relative to the corresponding lenses? (b) What is the total magnification? (c) What is the height of the final image?
An object is located \(16.0 \mathrm{cm}\) in front of a converging lens with focal length \(12.0 \mathrm{cm} .\) To the right of the converging lens, separated by a distance of \(20.0 \mathrm{cm},\) is a diverging lens of focal length \(-10.0 \mathrm{cm} .\) Find the location of the final image by ray tracing and verify using the lens equations.
A cub scout makes a simple microscope by placing two converging lenses of +18 D at opposite ends of a \(28-\mathrm{cm}^{-}\) long tube. (a) What is the tube length of the microscope? (b) What is the angular magnification? (c) How far should an object be placed from the objective lens?
The eyepiece of a microscope has a focal length of \(1.25 \mathrm{cm}\) and the objective lens focal length is \(1.44 \mathrm{cm} .\) (a) If the tube length is \(18.0 \mathrm{cm},\) what is the angular magnification of the microscope? (b) What objective focal length would be required to double this magnification?
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