Magnification

Definition of Magnification

Magnification is the ratio of the size of an image to the size of the object producing the image. It tells us how much larger or smaller the image is compared to the object.

It is a dimensionless quantity, meaning it has no units because it is a ratio of two lengths measured in the same units.

If the magnification is greater than 1, the image is larger than the object (enlarged). If it is less than 1, the image is smaller than the object (reduced).

Calculating Magnification

The formula to calculate magnification is:

$$\text{Magnification} = \frac{\text{Image height}}{\text{Object height}}$$

It is important to use consistent units for both image height and object height (e.g., both in centimetres or both in millimetres).

Magnification can be:

• Greater than 1: image is larger than the object
• Equal to 1: image is the same size as the object
• Less than 1: image is smaller than the object

The magnification value also helps describe the image orientation (see next section).

For instance, if an object is 4 cm tall and the image formed is 8 cm tall, the magnification is:

$$\text{Magnification} = \frac{8\,\text{cm}}{4\,\text{cm}} = 2$$

This means the image is twice as tall as the object.

Types of Images and Magnification

Images can be either real or virtual:

• Real images are formed when light rays actually meet. They can be projected onto a screen.
• Virtual images are formed when light rays appear to come from a point but do not actually meet. They cannot be projected onto a screen.

Images can also be inverted (upside down) or upright (same orientation as the object).

The sign of magnification indicates the orientation of the image:

• Positive magnification means the image is upright.
• Negative magnification means the image is inverted.

For example, if the magnification is -0.5, the image is half the size of the object and inverted.