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Ch 34: Ray Optics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 34: Ray OpticsProblem 8
Chapter 34, Problem 8

When you look into your car's 5.0-cm-tall rear-view mirror from 35 cm away, the front of a bus, from the ground to the roof, exactly fills the mirror. If the bus is 17 m from the mirror, how tall is the bus?

Verified step by step guidance
1
Understand the problem: The rear-view mirror acts as a plane mirror, and the height of the image in the mirror is proportional to the height of the object (the bus) based on the geometry of similar triangles. We are tasked with finding the height of the bus.
Set up the relationship using similar triangles: The height of the image in the mirror (5.0 cm) and the height of the bus (h) are proportional to their respective distances from the mirror. The distance of the image is the distance from the observer to the mirror (35 cm), and the distance of the bus is 17 m (convert to cm: 1700 cm).
Write the proportionality equation: \( \frac{\text{Height of image}}{\text{Distance to image}} = \frac{\text{Height of object}}{\text{Distance to object}} \). Substituting the known values, \( \frac{5.0}{35} = \frac{h}{1700} \).
Solve for the height of the bus (h): Rearrange the equation to isolate \( h \): \( h = \frac{5.0 \times 1700}{35} \).
Perform the calculation to find \( h \): Simplify the expression \( h = \frac{5.0 \times 1700}{35} \) to determine the height of the bus in cm, and convert the result to meters if needed.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Similar Triangles

The concept of similar triangles states that if two triangles have the same shape, their corresponding angles are equal, and the lengths of their corresponding sides are proportional. In this scenario, the rear-view mirror and the bus form two similar triangles, allowing us to set up a proportion to find the height of the bus based on the height of the mirror and the distances involved.
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Proportional Relationships

Proportional relationships occur when two quantities maintain a constant ratio. In this problem, the height of the bus and the height of the mirror can be related through their respective distances from the observer. By establishing a ratio between the height of the mirror and the height of the bus, we can solve for the unknown height of the bus using the distances provided.
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Distance and Magnification

Distance and magnification are key in understanding how objects appear in mirrors. The apparent size of an object in a mirror is influenced by the distance from the observer to the mirror and the object itself. In this case, the distances from the mirror to the observer and the bus help determine how the bus's height can be calculated based on the mirror's height and the distances involved.
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Related Practice
Textbook Question

A 5.0-cm-thick layer of oil is sandwiched between a 1.0-cm-thick sheet of glass and a 2.0-cm-thick sheet of polystyrene plastic. How long (in ns) does it take light incident perpendicular to the glass to pass through this 8.0-cm-thick sandwich?

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Textbook Question

It is 165 cm from your eyes to your toes. You're standing 200 cm in front of a tall mirror. How far is it from your eyes to the image of your toes?

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Textbook Question

At what angle ϕ should the laser beam in FIGURE EX34.6 be aimed at the mirrored ceiling in order to hit the midpoint of the far wall?

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Textbook Question

A 1.0-cm-thick layer of water stands on a horizontal slab of glass. A light ray in the air is incident on the water 60° from the normal. What is the ray's direction of travel in the glass?

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Textbook Question

A costume jewelry pendant made of cubic zirconia is submerged in oil. A light ray in the oil strikes one face of the zirconia crystal at an angle of incidence of 25°. Once inside, what is the ray's angle with respect to the face of the crystal?

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Textbook Question

The mirror in FIGURE EX34.5 deflects a horizontal laser beam by 60°. What is the angle ϕ?