10.1.3

# Lenses

Test yourself

## Converging lenses

A converging or convex lens takes rays of light and focuses them at a point. The rays converge.

### Converging light

• If rays enter a converging lens parallel to its axis they will cross each other at a single point on the other side of the lens.
• The is called the focal point.
• If the rays do not come in parallel to the axis the image is formed in a different place.

### Image location

• The equation relating the image location to the object location and the focal point is:
• 1/the focal length = 1/the image distance + 1/the object distance
• $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
• Where u is the image distance, v is the object distance and f is the focal length.

## Diverging Lenses

A diverging or concave lens causes light to bend away from the axis, the light diverges.

### Diverging light

• If parallel rays enter the lens they are diverted away from the axis.
• This creates the illusion that the object is closer to the lens than it is.
• If the new rays are traced back they form an image at the focal point.

### Calculation

• The focal length can be calculated from the image and the object distance with the equation:
• 1/the focal length = 1/the image distance + 1/the object distance
• $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
• Where u is the image distance, v is the object distance and f is the focal length.

### Image location

• The diverging lens can appear confusing as the image and the object are on the same side of the lens.
• The image formed is virtual as the light rays do not actually meet, they just appear to.

## Lens Power

The power of a lens is related to how 'quickly' it can focus light.

### Bending light

• A lens will change the direction of light so that all the rays cross at a point and create an image.
• The incoming rays are parallel to the axis they will focus at the focal point.
• The closer the focal point is to the lens the more powerful the lens.

### Calculation

• The equation for the power of a lens is given by:
• Power = $\frac{1}{the \;focal\; length}$
• $P=\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
• P is the power.
• u is the image distance.
• v is the object distance.
• f is the focal length.