# Physics Lesson 12.9.8 - Combined Systems of Lenses and Curved Mirrors

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

## Combined Systems of Lenses and Curved Mirrors

We can combine optical tools such as plane and curved mirror with lenses to produce new optical systems, like we did in the previous tutorial where two curved mirrors were combined to produce new images. Let's see an example in this regard.

### Example 3

An optical magnifying device is composed by a converging lens and a concave mirror as shown in the figure. What is the total magnification produced by this optical system if the object is placed at the distance shown?

### Solution 3

First, let's calculate the position of the image produced by the converging lens. From the figure, we can extract the following clues:

do = 22 cm - 16 cm = 6 cm
FL = 8 cm
dî = ?

Applying the equation

1/do + 1/dî = 1/FL

we obtain

1/6 + 1/dî = 1/8
1/dî = 1/8 - 1/6
= 3/24 - 4/24
= - 1/24

This means the image produced by the converging lens is 24 cm on its left. Thus, the magnification produced by the converging lens is

ML = di/do
= - 24/6
= - 4

This means the image produced by the converging lens is 4 times larger than the object.

This image acts as an object for the concave mirror. Its distance from the mirror is

do = 16 cm + 24 cm = 40 cm
F = 20 cm
dî = ?

We have:

1/do + 1/dî = 1/FM
1/40 + 1/dî = 1/20
1/dî = 1/20 - 1/40
= 2/40 - 1/40
= 1/40

Thus, the second image is 40 cm on the left of the converging lens. In this case, there is no magnification as

MM di/do
= 40/40
= 1

Thus, the mirror is used only to turn the image upright.

Therefore, the total magnification produced by this system is

Mtotal = ML × MM
= - 4 × 1
= - 4

This means the final image is 4 times larger than the object.

You have reached the end of Physics lesson 12.9.8 Combined Systems of Lenses and Curved Mirrors. There are 8 lessons in this physics tutorial covering Lenses. Equation of Lenses. Image Formation of Lenses, you can access all the lessons from this tutorial below.

## More Lenses. Equation of Lenses. Image Formation of Lenses Lessons and Learning Resources

Optics Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
12.9Lenses. Equation of Lenses. Image Formation of Lenses
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
12.9.1What Are Lenses? Types of Lenses
12.9.2Special Rays in Lenses
12.9.3Image Formation in Converging Lenses
12.9.4Image Formation in Diverging Lenses
12.9.5Equation of Lenses
12.9.6Magnification Produced by Lenses
12.9.7Aberration in Lenses
12.9.8Combined Systems of Lenses and Curved Mirrors

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