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Chapter 2: Problem 14

You can argue that a flat piece of glass, such as in a window, is like a lens with an infinite focal length. If so, where does it form an image? That is, how are \(d_{\mathrm{i}}\) and \(d_{\mathrm{o}}\) related?

Short Answer

Expert verified
The relationship between the object distance (\(d_o\)) and image distance (\(d_i\)) for a flat piece of glass, like a window, which can be considered as a lens with infinite focal length, can be obtained using the thin lens equation. By setting the focal length to infinity, we simplify the equation and obtain the result: \(d_i = -d_o\). This indicates that the image formed by a flat piece of glass is at the same distance from the glass as the object, but on the opposite side (negative sign).

Step by step solution

01

Understand the Thin Lens Equation

The thin lens equation relates the object distance (do), image distance (di), and focal length (f) of a lens. The equation is given by: \[\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\] In this problem, we are considering a flat piece of glass as a lens with an infinite focal length. Therefore, we will set the focal length, f, to infinity.
02

Set the Focal Length to Infinity

Since we are considering the flat piece of glass as a lens with an infinite focal length, we need to set f to infinity in the thin lens equation: \[\frac{1}{\infty} = \frac{1}{d_o} + \frac{1}{d_i}\]
03

Simplify the Equation

Now, simplify the equation. Since 1/∞ is essentially 0, the equation becomes: \[0 = \frac{1}{d_o} + \frac{1}{d_i}\]
04

Solve for Image Distance (di)

To find the relationship between the object distance (do) and image distance (di), we can solve the simplified thin lens equation for di: \[\frac{1}{d_i} = -\frac{1}{d_o}\] Now, multiply both sides of the equation by \(d_o d_i\): \[d_o d_i = -d_o^2\] Finally, divide both sides of the equation by \(d_o\): \[d_i = -d_o\]
05

Interpret the Result

The result, \(d_i = -d_o\), tells us that the image formed by a flat piece of glass is at the same distance from the glass as the object, but on the opposite side (negative sign). So, for a flat piece of glass, like a window, the image is formed at an equal distance on the other side of the glass.

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Most popular questions from this chapter

What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person's face is \(12.0 \mathrm{cm}\) away? Explicitly show how you follow the steps in the Problem-Solving Strategy: Spherical Mirrors.

The power for normal close vision is 54.0 D. In a vision-correction procedure, the power of a patient's eye is increased by 3.00 D. Assuming that this produces normal close vision, what was the patient's near point before the procedure?

An object of height \(3.0 \mathrm{cm}\) is placed at \(5.0 \mathrm{cm}\) in front of a diverging lens of focal length \(20 \mathrm{cm}\) and observed from the other side. Where and how large is the image?

An object of height 2 \(\mathrm{cm}\) is placed at \(50 \mathrm{cm}\) in front of a diverging lens of focal length \(40 \mathrm{cm} .\) Behind the lens, there is a convex mirror of focal length \(15 \mathrm{cm}\) placed 30 cm from the converging lens. Find the location, orientation, and size of the final image.

Suppose a 200 mm-focal length telephoto lens is being used to photograph mountains \(10.0 \mathrm{km}\) away. (a) Where is the image? (b) What is the height of the image of a \(1000 \mathrm{m}\) high cliff on one of the mountains?
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