P8.3 – Thin Converging Lens

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1. Describe the action of a thin converging lens on a beam of light using ray diagrams.

A lens is a transparent object that causes the light that passes through it to refract. A converging lens that is curved on both sides (there are two types of converging lens- concave and convex.)

A converging lens causes the light rays that are travelling parallel to its principal axis to refract and cross the principal axis at a fixed point called the focal point. (This is explained in more detail below).

(A ray diagram is given below)

It should also be noted that converge is a word that describes the tendency of two lines to meet.

 

2. Use the terms principal focus and focal length.

Principal focus or the focal point is the point where rays of light travelling parallel to the principal axis intersect the principal axis and converge.

Focal length is the distance between the centre of the lens and the focal point.

 

 

3. Draw and interpret simple ray diagrams that illustrate the formation of real and virtual images by a single converging lens.

Based on where the object is placed, the image formed could be inverted/upright, real/virtual and reduced/enlarged.

Inverted means that the image is upside down and upright obviously means that the image is the right way up.

Real images are formed on a screen (or another detector, like your eyes) when all of the light rays from a single point on an object hits a single point on the screen. In virtual images, on the other hand, are produced when light enters our eyes that appear to come from a real object when in reality, there is no object at the apparent source. This is explained in Unit P8.1 too.

Reduced means that the image is smaller than the object and enlarged means that the image is larger than the object.

The position of the object is described in terms of the number of focal lengths between the optic centre and the object.

There are also some important things you should note when drawing ray diagrams:

According to the system you follow, some of the notation may differ, but for the IGCSE examinations, these are the rules:

Light rays are always drawn as straight lines with arrows along them.  Virtual light rays are drawn the same way, but instead of a solid line, the line is dashed. The arrows show us which direction the rays travel in.

You will also see some diagrams where they simply draw a line to represent the lens, however, how the light rays are refracted will change according to whether the lens is convex or concave. This is why it is important you always draw the shape of the lens. You should also draw a dashed vertical line up through the centre of the lens.

Next, we use arrows to represent the object and the image. The object arrow is always upright, and the direction of the image arrow changes according to the position of the object relative to the lens. To help us differentiate the object arrow and the image arrow, we denote them using OB and IM – OB for object (O is written where the arrow starts and B is written at the arrowhead) and IM for image (I is written where the arrow starts and M is written at the arrowhead). It should also be noted that the arrow that represents a virtual image must be made of a dashed line.

In addition, a distance of one focal length from the optic centre is written as F, two focal lengths is 2F, three is 3F, etc. This distance is always measured along the principal axis.

Unfortunately, I couldn’t find diagrams for every case that follows all of these rules, so you’ll have to learn them with a pinch of salt.

When the object is more than 2 focal lengths away from the optic centre, the image formed will be inverted, reduced and real.

 

You should know that when the arrow representing the image points down, it tells us that the image is inverted. When it goes up, it tells us that the image is upright.

When the object is at 2F, the image is inverted, the same size, and real.

 

 

When the object is between F and 2F, the image formed will be inverted, enlarged and real.

 

When the object is at F, no image is formed because the rays do not converge or diverge.

 

Note that the lens is called biconvex because it is convex on both sides.

When the object is less than 1 focal length away from the optic centre, the image formed will be upright, enlarged and virtual.

 

 

Here, our brains trick us into thinking that the rays came from a single point, the object – it creates a fake source point and thus a virtual image is formed.

This is how magnifying glasses work. The image is on the same side as the object (there is no mirror image) and it is enlarged and upright.

 

4. Draw ray diagrams to illustrate the formation of a real image by a single lens.

Learn all the diagrams above apart from the last one.

In case you have trouble remembering how to draw them during the exam, and don’t know where to place the image or how the rays bend, here are some rules to remember:

The light rays always start from the object – so the arrows along the rays should always point away from the object. (In case you were confused, no – the object does not emit light. We see objects because it reflects light from a light source to our eyes. But this is not relevant to these ray diagrams, so we draw the light rays so that they start from the object.) Also, we draw the diagrams so that the rays start from the top of the object only. This makes the diagram simpler and easier to understand. If we tried to draw rays from every point of the object, we would be here all day and the diagram would be too busy to understand.

When the incident ray travels parallel to the principal axis, it is refracted so that the refracted ray will intersect the principal axis at F on the other side (refer to the diagrams above).

When the incident ray intersects F on the principal axis before reaching the lens, it is refracted so that the refracted ray travels parallel to the principal axis.

When the incident ray intersects the optic centre of the lens, its direction does not change.

Following these rules and, provided that you draw the diagram to scale, you can find where the image is formed, whether it is reduced or enlarged and whether it is upright or inverted by finding the point that the light rays intersect.

 

 

Notes submitted by Lintha and edited by Sarah.

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