# Physics Lesson 12.9.5 - Equation of Lenses

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Welcome to our Physics lesson on Equation of Lenses, this is the fifth 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.

## Equation of Lenses

The equation of lenses is identical to that of curved mirrors. Thus, if we denote by do the position of object in respect to the lens, by dîthe position of image and by F the focus (focal length), we obtain

1/do + 1/dî = 1/F

The sign rules are identical to those used in spherical mirrors, i.e.

1. The object's distance do is always taken as positive.
2. The image's distance dîis taken as positive when the image is real, otherwise it is negative.
3. Focal length F is positive for converging lenses and negative for diverging ones.

### Example 2

An object is placed 12 cm on the left of a converging lens of focal length equal to 8 cm.

1. What type of image is produced?
2. What is the position of image in respect to the lens?

### Solution 2

1. From the description it is clear that this is an example of 3rd case of image formation in converging lenses as the object is between F and 2F (12 is between 8 and 16). Therefore, the image is real, inverted and magnified. It is formed beyond C = 2F on the right of the lens.
2. We use the lenses equation
1/do + 1/dî = 1/F

to find the position of image in respect to the lens. Thus, substituting the values (given that do = + 12 cm and F = + 8 cm) we obtain

1/12 + 1/dî = 1/8
1/dî = 1/8 - 1/12
= 3/24 - 2/24
= 1/24

Therefore dî= 24 cm. This result means the image is produced at 24 cm on the right of the lens as shown in the figure below. You have reached the end of Physics lesson 12.9.5 Equation of Lenses. 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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6. Continuing learning optics - read our next physics tutorial: Power of Lenses. The Human Eye

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