# The lens formula

##### Class Practical

Making rough measurements to check the validity of a lens formula.

#### Apparatus and materials

Convex lens

Retort stands and bosses, 2

Lamp with holder

Power supply, low voltage, 6 V

Metre rule

Screen, white

Calculator

#### Health & Safety and Technical notes

Read our standard health & safety guidance

The lamp, if run at 12 volts, is too bright for viewing directly when looking at virtual images. It works well operated at 6 volts instead of 12.

Alternatively, you can use a pea-lamp, i.e. a round MES bulb.

If you have a telescope mount it makes a useful and cheap optical bench for these measurements.

#### Procedure

**a** Tell students that for a simple lens the object distance, *u*, and image distance, *v*, are known to be related. Give them the appropriate formula for the convention you are using:

1/*u* + 1/*v* = 1/*f* for *'real is positive'*

or 1/*u* + 1/*f* = 1/*v* for *'Cartesian'*

Tell students that the constant 1/*f* is a property of lenses. It can be predicted by using geometry from knowledge of the way in which rays of light are bent at each surface of a lens. Or, 1/*f* can be predicted from the way in which a whole lens always bends a fan of rays to pass through an image point. Or, 1/*f* could be extracted from a large number of experimental measurements.

**b** Set up the lamp and screen on the axis of the lens with the lamp. Move them to obtain a clear image of the lamp filament on the screen. Measure *v* and *u*.

**c Real is positive** - Calculate the value of 1/*u* + 1/*v* (both positive). Repeat for several different values of *u*. Does this always give about the same value?

**Cartesian** - Give students the focal length of the lens being used. If you add the power of the lens 1/*f* (positive) to 1/*u* (which is negative), does it always give you 1/*v* (positive)? Repeat for several different values of *u*.

**d** Move the lamp or a piece of paper with a vertical arrow on it much closer to the lens so that a real image cannot be formed. This should be at an object distance of about half the focal length of the lens. Look at the virtual image of the lamp through the lens. Place a retort stand behind the lamp and move it till the virtual image of the lamp appears to be near it. (See Teaching note **2**.)

Measure *u* and *v* (now a negative value) and try them in the same formula. Repeat for one or two different lamp positions.

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Teaching notes

**1** The aim of this experiment is to provide an amusing game that will give students practice in locating virtual images. It is not to bring out the formula and make it important in the teaching. Virtual images cannot be caught on a screen.

**2** The 'catcher' for the virtual image in part **d** may be a tall retort stand seen above the lens. It is moved until the virtual image seen by one eye, and the stand seen by the other eye, seem to be in focus together, and remain together as the observer wags his/her head.

**3** Use a calculator to calculate the reciprocal values. Putting the values into the lens equation (real is positive) do not appear to fit until the image distance is given a negative sign.

*This experiment was safety-checked in January 2007*