# 5.22 The Lens Equation

## The Lens Equation

• This equation can be applied to all thin converging and diverging lenses
• The equation relates the focal length of the lens to the distances from the lens to the image and the object

• Where:
• = focal length (m)
• v = image distance from lens (m)
• u = object distance from lens (m)

• This equation only works for thin converging or diverging lenses
• The values are positive if the image is real

#### Worked example

A student investigates the focal length of a thin lens by using it to project and image onto a screen.

The object is set 50.0 cm from the centre of the lens and the screen moved back and forth until the inverted image is sharp. This position is found to be 75.0 cm from the lens.

Determine the focal length of the lens.

Step 1: Write the known values

• Distance from object to lens, u = 50.0 cm
• Distance from image to lens, v = 75.0 cm

Step 2: Write the equation and substitute in the values

f = 30 cm

#### Exam Tip

It is easy to forget the last step in a calculation like this one. Remember that you are calculating  not f, and that you need to take the reciprocal of your answer.

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