NameSkill Sheet 173Thin Lens FormulaHere You

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Skill Sheet 17.3

Thin Lens Formula

Here you will become familiar and practice with a mathematical formula called “the thin lens formula.” This formula gives scientists a way to calculate the location and the size of an image that is produced by a lens.

1. What is the thin lens formula?
When you use the thin lens formula, you assume that the thickness of the lens is very small compared with the distance between the lens and the object or the image. The formula applies both to convex or converging lenses and concave or diverging lenses. Converging lenses are thicker in the center than in the edges. Diverging lenses are thinner in the center than in the edges. The thin lens formula is:

Some important rules in using the thin lens formula:
•

Object distance, d0, is positive to the left of the lens and negative to the right of the lens.

•

Image distance, di, is negative to the left of the lens and positive to the right of the lens.

•

Positive d0, di indicates real object or image.

•

Negative d0, di indicates virtual object or image.

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Skill Sheet 17.3 Thin Lens Formula

2. Examples in using the thin lens formula
If you are using a convex lens, what happens an image when the object is very far from the lens? In other words, what happens when d0 is a large number?
Graphically, we see that as d0 increases, the image becomes smaller as it gets closer to the focal point. We can see this by using the thin lens formula with a lens that has a focal length equal to 5 centimeters.

If d0 =

then...

di =

8 cm,

1
---- = 1--- – 1--- = 0.2 – 0.125 = 0.075 di 5 8

1 - = 13.3 cm
-----------0.075

100 cm,

1- = 1--- – -------1 - = 0.2 – 0.01 = 0.19
--di
5 100

1 - = 5.26 cm
--------0.19

1,000 cm,

1
1 - = 0.2 – 0.001 = 0.199
---- = 1--- – ------------di
5 1,000

1 - = 5.03 cm
-----------0.199

If you are using a concave lens, you use a negative value for the focal length, f. In this case, the resulting image distance is a negative number indicating a virtual