Lenses, ray diagrams and magnification

​​In a nutshell

Lenses change the direction of light rays to converge or diverge. They are used to form real or virtual images. The result of light passing through a lens can be represented using a ray diagram.

Definitions

Equations

​$$magnification = \frac{image\: height}{object\: height}$$​​

Variable definitions

Types of lenses

A lens is a specifically shaped piece of glass that refracts light rays when they pass through it. Lenses refract light rays so that they change direction. This makes objects appear differently to what they actually are.

There are two types of lenses: convex and concave.

Convex lens

A convex lens bulges outwards towards the middle. It is also called a converging lens. This lens causes light parallel to the axis to converge at the principal focus.

1. Focal Point

Concave lens

A concave lens bends inwards towards the middle. It is also called a diverging lens. This lens causes light rays parallel to the axis to diverge. For a concave lens, the principal focus is where the rays diverging appear to have come from.

1. Focal Point

Rules for drawing ray diagrams

There are three rules for rays refracted by a lens. They describe how light rays behave after they pass through the lens.

Tip: Only two of these rays need to drawn to find the point at which they cross. The easiest rays to draw are 1 and 3 but feel free to use 2 if to double check!

Describing an image

​​Procedure

Ray diagrams

Ray diagrams can be constructed for light from an object passing through a convex or concave lens.

Convex ray diagram

Concave ray diagram

There are a set of steps to follow for drawing a ray diagram for each lens. 

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Convex lens

Procedure

1.	Draw a ray of light going from the top of the object to the lens, parallel to the axis. The first rule for rays says that this will pass through the principal focus ($$F$$​). Draw the ray going through the principal focus.	​
2.	Draw a ray going from the top of the object passing through the middle of the lens. The third rule for rays says that this should continue on the same path. Draw the ray continuing on this path.
3.	Mark the point where the two lines meet. This is the top of the image.
4.	Repeat the past three steps for the bottom of the image. If the bottom of the object is on the axis, the bottom of the image will also be on the axis.

Note: $$F$$​ is used to label the principal focus on both sides. $$2F$$​ means twice the focal length away from the lens. The axis can be thought of as like the $$x$$​-axis of a graph.

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The distance the object is placed from the lens will affect the type of image created. If the object is placed closer to the lens than the principal focus, a virtual image will be formed.

An image can be determined as virtual as the rays on the refracted side of the lens won't meet at a point - they diverge. To construct a virtual image, continue the path of the rays (as dotted lines) on the object side of the lens. They should meet at a point.

Concave lens

PROCEDURE

1.	Draw a ray of light going from the top of the object to the lens, parallel to the axis. The first rule for rays says that this will appear to have come from the principal focus ($$F$$​). Draw a dotted line from the left-hand side's principal focus to the ray. Then draw a normal line continuing on this path.	​
2.	Draw a ray going from the top of the object passing through the middle of the lens. The third rule for rays says that this should continue on the same path. Draw the ray continuing on this path.
3.	The two rays won't meet on the other side of the lens. Instead mark where the two lines intersect (meet) on the object's side.
4.	Repeat the past 3 steps for the bottom of the image. If the bottom of the object is on the axis, the bottom of the image will also be on the axis.

Concave lenses always create virtual images, no matter the distance from the lens.

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Magnification

The magnification is measured as the relative size of the image compared to the size of the object.

​$$magnification = \frac{image\: height}{object\: height}$$​​

This gives the magnification produced by a lens at a given distance.

Tip: To find the magnification of a lens, a ruler can be used to measure the object height and the image height!