A dentist holds a small mirror 1.9 cm from a surface of a patient's tooth. The image formed is u

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A dentist holds a small mirror 1.9 cm from a surface of a...

A dentist holds a small mirror $1.9 \mathrm{cm}$ from a surface of a patient's tooth. The image formed is upright and 5.0 times as large as the object. (a) Is the image real or virtual? (b) What is the focal length of the mirror? Is it concave or convex? (c) If the mirror is moved closer to the tooth, does the image get larger or smaller? (d) For what range of object distances does the mirror produce an upright image?

Key Concepts

Relationship between Object Distance and Image Size

Changing the distance between the object and the mirror influences the size of the image. In mirror systems, as the object moves closer or further from the mirror, the corresponding image size and its characteristics (such as being magnified or reduced) change. This relationship is key to predicting image behavior when the object distance varies, especially in systems where the image’s orientation (upright or inverted) can change.

Concave versus Convex Mirrors

Concave mirrors are curved inward like the inside of a bowl and can produce both real and virtual images depending on the object’s distance relative to the focal length. Convex mirrors are curved outward and only produce virtual, reduced, and upright images. Understanding the difference between these mirrors is essential for analyzing how they form images under various conditions.

Real versus Virtual Images

Real images are formed when light rays converge at a point, and they are typically inverted. Virtual images occur when the reflected rays appear to diverge from a common point behind the mirror, and these images are upright. The type of image produced depends on the object’s position relative to the focal length as well as the mirror’s curvature.

Mirror Equation and Gaussian Sign Convention

This concept involves the equation 1/f = 1/do + 1/di, where f represents the focal length of the mirror, do is the object distance, and di is the image distance. The sign conventions determine whether the distances or focal lengths are positive or negative, which helps in identifying whether an image is real or virtual and whether a mirror is concave or convex.

Magnification

Magnification (m) is the ratio of the image height to the object height, and it is given by m = -di/do. The negative sign accounts for image inversion. A positive magnification indicates an upright image, while a negative value corresponds to an inverted image. Understanding magnification is crucial for relating image size to object distance in mirror systems.

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