Physics Lesson 12.8.6 - Equation of Curved Mirrors

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Welcome to our Physics lesson on Equation of Curved Mirrors, this is the sixth lesson of our suite of physics lessons covering the topic of Mirrors. Equation of Curved Mirrors. Image Formation in Plane and Curved Mirrors, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Equation of Curved Mirrors

There is an equation that provides the numerical relationship between the object's distance d_o, image distance dî and focal length (focus) F, which allows us to determine the position of image without having need for drawings. This equation (known as the Equation of Curved Mirrors) is

However, this is not that simple; not always all values are positive. Thus, we need to correctly apply the sign rules if we want to avoid mistakes in the position values. These rules are provided below.

1. The object's position d_o is always taken as positive.
2. In concave mirrors, the focal length F is taken as positive while in convex mirrors it is taken as negative.
3. If the image is real, its position dî is taken as positive, while if the image is virtual its distance dî is taken as negative.

Example 2

An object is placed 12 cm in front of a concave mirror of focal length equal to 18 cm.

1. What are the image features for this case?
2. What is the position of image formed in this mirror?

Solution 2

1. From the given values, it is clear that the image is formed nearer to the concave mirror than focus. Therefore, this situation represents the fifth case of image formation in concave mirrors. It means the image is virtual, erect and enlarged.
2. We have the following clues based on the description and the sign rules of image formation in curved mirrors.

Applying the mirror equation

we obtain after substitutions

Therefore, the position of image is d_î = -36 cm. This means it is formed at 36 cm behind the mirror, as shown in the figure below.

You have reached the end of Physics lesson 12.8.6 Equation of Curved Mirrors. There are 8 lessons in this physics tutorial covering Mirrors. Equation of Curved Mirrors. Image Formation in Plane and Curved Mirrors, you can access all the lessons from this tutorial below.

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