Mirror Equation Video Lessons

Concept

# Problem: The writing on the passenger-side mirror of your car says "Warning! Objects in mirror are closer than they appear"(Figure 1) . There is no such warning on the driver's mirror. Consider a typical convex passenger-side mirror with a focal length of -80 cm. A 1.5-m-tall cyclist on a bicycle is 28 m from the mirror. You are 1.4 m from the mirror, and suppose, for simplicity, that the mirror, you, and the cyclist all lie along a line.Part AHow far are you from the image of the cyclist?Express your answer to two significant figures and include the appropriate units.Part BHow far would you have been from the image if the mirror were flat?Express your answer to two significant figures and include the appropriate units.Part CWhat is the image height?Express your answer to two significant figures and include the appropriate units.Part DWhat would the image height have been if the mirror were flat?Express your answer to two significant figures and include the appropriate units.Part EWhy is there a warning label on the passenger-side mirror?The mirror at the passenger's side is often convex to make the viewing angleThe image is than the object and so the driver might think that the object is at greater distance than it is in reality, so if driver stop suddenly thinking the cyclist will have time to stop also, he might be unpleasantly surprised.

###### FREE Expert Solution

The mirror equation:

$\overline{)\frac{\mathbf{1}}{{\mathbf{s}}_{\mathbf{o}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{s}}_{\mathbf{i}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{f}}}$

Part A

1/28 + 1/si = 1/-0.80

1/si = 1/-0.80 - 1/28 = - 9/7

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###### Problem Details

The writing on the passenger-side mirror of your car says "Warning! Objects in mirror are closer than they appear"(Figure 1) . There is no such warning on the driver's mirror. Consider a typical convex passenger-side mirror with a focal length of -80 cm. A 1.5-m-tall cyclist on a bicycle is 28 m from the mirror. You are 1.4 m from the mirror, and suppose, for simplicity, that the mirror, you, and the cyclist all lie along a line.

Part A

How far are you from the image of the cyclist?

Express your answer to two significant figures and include the appropriate units.

Part B

How far would you have been from the image if the mirror were flat?

Express your answer to two significant figures and include the appropriate units.

Part C

What is the image height?

Express your answer to two significant figures and include the appropriate units.

Part D

What would the image height have been if the mirror were flat?

Express your answer to two significant figures and include the appropriate units.

Part E

Why is there a warning label on the passenger-side mirror?

The mirror at the passenger's side is often convex to make the viewing angle

The image is than the object and so the driver might think that the object is at greater distance than it is in reality, so if driver stop suddenly thinking the cyclist will have time to stop also, he might be unpleasantly surprised.