# 5.23 Magnification

## Magnification

#### Magnification as a Ratio of Heights

• Magnification means how much larger the image is than the object
• This is the ratio of the image/object height

• Where:
• m = magnification
• hi = image height (m)
• ho = object height (m)

#### Magnification as a Ratio of Distances

• A diagram of an object and its real image will produce similar triangles
• Therefore, the ratio of magnification is also represented by comparing distance from the lens to the object and the image

• This also works for virtual images

• Where:
• m = magnification
• v = distance from lens to image (m)
• u = distance from lens to object (m)
• Since magnification is a ratio, it has no units

#### Worked example

A magnifying glass has a focal length of 15 cm. It is held 5 cm away from a component which is being examined.

Determine the magnification of the image.

Step 1: Write the known values

• Focal length, f = 15 cm
• Distance between object and lens, u = 5 cm

Step 2: Use the lens formula and rearrange to make v the subject

• The negative sign indicates a virtual image (expected for a magnifying glass) and is ignored for the next step

Step 3: Use the magnification formula to find the magnification of the image

#### Worked example

A person sees an image from a magnifying glass.Calculate the magnification of this image. Clearly show your working on the diagram.

Step 1: Measure the height of the object from the scale

The object is 10 cm

Step 2: Measure the height of image from the scale

The image is 20 cm

Step 3: Substitute values into the magnification equation

#### Exam Tip

The most common mistake with magnification calculations is to get the formula upside down.

Do a 'sanity check' by looking at the answer to make sure that magnified objects have got bigger (m > 1) and diminished ones smaller (m < 1).

Since we are working with ratios (so the units get cancelled out) this is one of those rare times when you don't need to convert everything to SI units, but do check that your units are all the same - for example all distances in cm.

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