Ch. 32 - Light: Reflection and Refraction

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 32 - Light: Reflection and Refraction

Problem 29

Chapter 31, Problem 29

When walking toward a concave mirror you notice that your image flips at a distance of 0.80 m from the mirror. What is the radius of curvature of the mirror? [Hint: Carefully examine Section 32–4.]

Verified step by step guidance

Understand the problem: The image flipping indicates that the object (you) is moving through the focal point of the concave mirror. At this point, the image changes from real to virtual or vice versa. The distance given (0.80 m) is the focal length \( f \) of the mirror.

Recall the relationship between the focal length \( f \) and the radius of curvature \( R \) for a concave mirror. This is given by the formula: \( f = \frac{R}{2} \).

Rearrange the formula to solve for the radius of curvature \( R \): \( R = 2f \).

Substitute the given focal length \( f = 0.80 \; \text{m} \) into the equation: \( R = 2 \times 0.80 \; \text{m} \).

Conclude that the radius of curvature \( R \) can be calculated by multiplying the focal length by 2. Perform the multiplication to find the final value if needed.

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Key Concepts

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

Concave Mirror

A concave mirror is a spherical mirror that curves inward, resembling a portion of a sphere. It can produce real and virtual images depending on the object's distance from the mirror. When an object is placed within the focal length, the image appears upright and magnified, while beyond the focal point, the image is inverted and reduced in size.

Radius of Curvature

The radius of curvature is the distance from the mirror's surface to its center of curvature, which is the center of the sphere from which the mirror is derived. For concave mirrors, the radius of curvature is related to the focal length, with the focal length being half of the radius. This relationship is crucial for determining the mirror's properties and the behavior of images formed.

Mirror Formula

The mirror formula relates the object distance (u), image distance (v), and the focal length (f) of a mirror, expressed as 1/f = 1/v + 1/u. This formula is essential for solving problems involving mirrors, as it allows for the calculation of distances and the understanding of how images are formed based on the object's position relative to the mirror.

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Related Practice

Textbook Question

In Example 32–4, show that if the object is moved 10.0 cm farther from the concave mirror, the object’s image size will equal the object’s actual size. Stated as a multiple of the focal length, what is the object distance for this “actual-sized image” situation?

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Textbook Question

An object is placed a distance r in front of a wall, where r exactly equals the radius of curvature of a certain concave mirror. At what distance from the wall should this mirror be placed so that a real image of the object is formed on the wall? What is the lateral magnification of the image?

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Textbook Question

A shaving or makeup mirror is designed to magnify your face by a factor of 1.8 (when compared to a flat mirror) when your face is placed 20.0 cm in front of it.

(a) What type of mirror is it?

(b) Describe the type of image that it makes of your face.

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Textbook Question

A flashlight beam strikes the surface of a pane of glass (n = 1.56) at a 69° angle to the normal. What is the angle of refraction?

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Textbook Question

(II) Show, using a ray diagram, that the lateral magnification m of a convex mirror is m = -dᵢ/dₒ , just as for a concave mirror. [Hint: Consider a ray from the top of the object that reflects at the center of the mirror.]

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Textbook Question

Let the focal length of a convex mirror be written as ƒ = ―|ƒ|. Show that the lateral magnification m of an object a distance dₒ from this mirror is given by m = |ƒ| / (dₒ +|ƒ| ). Based on this relation, explain why your nose looks bigger than the rest of your face when looking into a convex mirror.

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