   Chapter 25, Problem 57PE

Chapter
Section
Textbook Problem

What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Explicitly show how you follow the steps in the Problem−Solving Strategy for Mirrors.

To determine

The focal length of a makeup mirror that produces a magnification of 1.50.

Explanation

Given info:

Magnification of the mirror, m=1.5

Object distance, d0=12.0cm

Formula used:

The expression for the magnification is,

m=did0    .......... (1)

Here,

• d0 is the object distance.
• di is the image distance.

The mirror formula can be expressed as,

1f=1di+1d0    .......... (2)

Calculation:

Strategies to solve the given problem are given below.

1. Collect the information given in the problem.
2. Find the distance of the image by using the expression of magnification as magnification and the distance of the object is given.
3. Use the expression of the mirror formula to calculate the focal length of the mirror.

Rearrange equation (1) for the image distance.

di=md0

Substitute 1.5 for m and 12cm for d0 in above expression

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