A dentist uses a spherical mirror that produces an upright...

Name: Problem 30, Chapter 23: College Physics
Uploaded: 2021-05-10T14:31:10-08:00
Duration: 1 min 33 s
Channel: Narayan Hari
Description: A dentist uses a spherical mirror that produces an upright image of a tooth that is magnified four times. (a) The mirror is (1) converging, (2) diverging, (3) flat. Explain. (b) What is the mirror's focal length in terms of the object distance?

A dentist uses a spherical mirror that produces an upright image of a tooth that is magnified four times. (a) The mirror is (1) converging, (2) diverging, (3) flat. Explain. (b) What is the mirror's focal length in terms of the object distance?

Key Concepts

Magnification

Magnification in mirror systems is defined as m = -di/do, indicating how the height of the image compares to the height of the object. The negative sign shows the inversion of the image. However, when the magnification is positive, as in the case of an upright image, it implies that the image is virtual. This concept is crucial for determining the correct positions of objects relative to the mirror’s focal point.

Virtual Image Formation

A virtual image is formed when the reflected rays diverge and appear to originate from a common point behind the mirror. In spherical mirror systems, virtual images are typically upright and magnified, and they occur when the object is placed between the focal point and the mirror. This concept is key in applications such as dentistry where a magnified, upright image is required.

Spherical Mirrors

Spherical mirrors are curved mirrors whose reflecting surfaces form a segment of a sphere. They are classified as converging (concave) or diverging (convex) based on whether they focus incoming parallel rays to a point or cause them to scatter. Understanding the type of spherical mirror is essential for predicting the image’s nature, such as whether the image is real or virtual.

Mirror Equation

The mirror equation, given by 1/f = 1/do + 1/di, relates the focal length (f) of the mirror to the object distance (do) and the image distance (di). This equation is fundamental for calculating unknown parameters of mirror optics, and it is particularly useful when analyzing the formation of magnified or reduced images.

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