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Chapter 2: Problem 38

Ray tracing for a flat mirror shows that the image is located a distance behind the mirror equal to the distance of the object from the mirror. This is stated as \(d_{i}=-d_{\mathrm{o}}\) since this is a negative image distance (it is a virtual image). What is the focal length of a flat mirror?

Short Answer

Expert verified
The focal length of a flat mirror is infinitely large or not applicable, as flat mirrors do not have a converging or diverging effect on light rays. They simply reflect light rays in a way that maintains parallelism between the incoming and outgoing rays. This can be shown using the mirror equation and substituting the given relationship between the object and image distances.

Step by step solution

01

1. Write down the mirror equation.

The mirror equation relates the object distance, image distance, and focal length of a mirror as: \[\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\] Where: - \(f\) is the focal length of the mirror - \(d_o\) is the object distance (distance from the object to the mirror) - \(d_i\) is the image distance (distance from the image to the mirror)
02

2. Substitute the relationship between the object and image distances.

Given that for a flat mirror, the image distance (\(d_i\)) is equal to the negative of the object distance (\(d_o\)), we can substitute this relationship into the mirror equation: \[\frac{1}{f} = \frac{1}{d_o} + \frac{1}{-d_o}\]
03

3. Simplify the equation and solve for the focal length.

Simplify the equation by combining the fractions on the right-hand side: \[\frac{1}{f} = \frac{1 - 1}{d_o}\] Now, the equation becomes: \[\frac{1}{f} = 0\] The only solution to this equation is if the focal length is infinitely large, or: \[f = \infty\]
04

4. Conclusion

The focal length of a flat mirror is infinitely large or not applicable since it doesn't have a converging or diverging effect on light rays, unlike curved mirrors. Flat mirrors simply reflect light rays in a way that maintains parallelism between the incoming and outgoing rays.

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Most popular questions from this chapter

Two convex lenses of focal lengths \(20 \mathrm{cm}\) and 10 \(\mathrm{cm}\) are placed \(30 \mathrm{cm}\) apart, with the lens with the longer focal length on the right. An object of height \(2.0 \mathrm{cm}\) is placed midway between them and observed through each lens from the left and from the right. Describe what you will see, such as where the image(s) will appear, whether they will be upright or inverted and their magnifications.

Why is your vision so blurry when you open your eyes while swimming under water? How does a face mask enable clear vision?

Some telephoto cameras use a mirror rather than a lens. What radius of curvature mirror is needed to replace a \(800 \mathrm{mm}-\) focal length telephoto lens?

What is meant by a negative magnification? What is meant by a magnification whose absolute value is less than one?

For normal distant vision, the eye has a power of 50.0 D. What was the previous far point of a patient who had laser vision correction that reduced the power of her eye by \(7.00 \mathrm{D},\) producing normal distant vision?
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