Textbook Question
A dentist wants a small mirror that, when 2.00 cm from a tooth, will produce a 3.0 x upright image. What kind of mirror must be used and what must its radius of curvature be?
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33. Geometric Optics
Mirror Equation
3:41 minutesProblem 29
Textbook Question
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 guidance1
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.
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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.
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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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