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Chapter 31: Problem 2

Under what circumstances will the image in a concave mirror be the same size as the object?

Short Answer

Expert verified
The object will be the same size as the image in a concave mirror if the object is placed at twice the focal length from the mirror.

Step by step solution

01

Understand the Properties of a Concave Mirror

A concave mirror is a spherical mirror that is curved inward. It can create images that are virtual or real, and these images can be smaller, larger, or the same size as the object depending on the object's location relative to the mirror's focal point.
02

Apply the Mirror Formula

The mirror formula is defined as \(1/f = 1/v + 1/u\), where f represents the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. Normally, to use this formula, we'd need to know the values of two of these three variables to solve for the third.
03

Set Object Distance Equal to Image Distance

Since we are interested in the situation where the object size is the same as the image size for a concave mirror, we need to set the object distance (u) equal to the image distance (v). Substituting v = u into the mirror formula, we get \(1/f = 1/u + 1/u\), which simplifies to \(1/f = 2/u\). From this, we can find that u = 2f or v = 2f, meaning that the object needs to be located at twice the focal length from the mirror.

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