Topic 4

What do mirrors and lenses do to light?

Light Rays

Light is an electromagnetic wave that travels in straight lines until it is either reflected or refracted.  We will look at the behaviour of light rays when:

• they are reflected in a mirror;

• refracted at a boundary.

We will explore different examples of reflection and the uses of refraction.

Reflection in a Flat Mirror

When light strikes a plane (flat) mirror, it is reflected as shown in the diagram:

We should note the following:

• There is an incident and reflected ray;

• The angle of incidence and the angle of refraction are measured from the normal line;

• The normal line is a construction line that is at 90 degrees to the surface of the mirror.

• The angle of incidence = angle of reflection.

  A common bear trap is to measure the angle of incidence or reflection from the surface of the mirror.  You must remember to measure from the normal.

Question 1  A light ray strikes a mirror at an angle to the surface of 30 degrees.  What is the angle of incidence?  What is the angle of reflection?  ANSWER

The Image in a Mirror

The picture below shows how the image in a mirror is formed.

We draw accurately two rays coming from the object and hitting the mirror at an angle.  Since angle of reflection = angle of incidence, the two rays will be reflected as shown.  We can then extend the rays back.  Where the two rays meet, that is where the corresponding part of the image is found.

You can see where this is done at the top and bottom of the image.

Question 2  What is the size of the object compared with the image?  ANSWER

There are two points to note about the image in a mirror:

• It laterally inverted.  This means that, although the image is the right way up compared with the object, left is swapped with right.

• It is virtual.  This means that if you look behind the mirror, you won't find the image there.

The picture below shows an example of lateral inversion:

Curved Mirrors

Concave Mirror

A concave mirror brings parallel rays of light together.

Each ray obeys the Law of Reflection.

Question 3  What is the Law of Reflection? ANSWER

Note how the shape of the mirror brings all the rays to a single point called the principal focus.  The distance between the principal focus and the surface of the mirror is called the focal length.

If the object is close up to the mirror, it appears the right way up (upright) and is magnified (made bigger).  If it's further away the image is upside down (inverted) and diminished (made smaller).

Other waves can be reflected by a concave mirror.  A satellite dish is a concave mirror to reflect microwave waves onto an antenna.  There was a device produced after the First World War to focus sound waves of incoming aircraft to give early warning of their presence.

Convex Mirror

A convex mirror reflects light rays outwards as shown in the diagram.

If we extend the rays behind the mirror, we see that they meet at a principal focus.  The image is virtual, upright, and diminished.

A convex mirror is used as a security mirror in a shop, or a wide angle mirror on a bus.

Question 4 checks if you are familiar with some of the terms used in reflection.

Refraction

When light hits an air-glass boundary, there are three things that happen to it:

• Some light is reflected;

• Some light is absorbed;

• Most of the light is transmitted.

If we shine a ray of light at an angle, we find something a little strange.  The ray does not carry on in a straight line as you might expect.  Instead it bends inwards.  This is called refraction.

Note the following:

• All angles are measured from the normal.

• The angle of incidence is greater than the angle of refraction.  The ray therefore bends towards the normal.

• When the ray emerges from the glass, it bends away from the normal.  The angle of refraction in this case is bigger than the angle of incidence.

Question 5  How does the path of the emergent ray compare with the path of the undeviated ray (the path the ray would have taken if the block hadn't been there)?  ANSWER

Refraction occurs because the speed of light in air is greater than the speed of light in glass.

For a prism, the ray diagram is like this, using a ray of monochromatic (single colour) red light.

Question 6.  How does the path of the emergent ray compare with the path of the undeviated ray?  ANSWER

If we use a ray of white light, we see that the light ray gets split into the colours of the rainbow (a spectrum).

This happens because red light is refracted less than blue light.

Lenses

Lenses are optical devices that bend light by refraction:

• In a converging (convex) lens, the light rays come together.

• In a diverging (concave) lens, the light rays spread apart.

Both types of lens have uses.

Converging Lens

The converging lens brings parallel rays of light onto a single point like this.

Note the following:

• There are two principal foci (plural of focus).  This is because the rays can come in either side of the lens.

• The focal length is the distance between the focus and the lens axis.  This is given the code F.  So 2F means twice the focal length.

The nature of the image depends on where the object is:

A real image can be projected onto a screen.

We can work out the magnification of the lens by the simple formula:

Question 7:  A converging lens magnifies an object 12 mm high so that it is projected onto a screen, and is 240 mm high.  What is the magnification?  Where is the object most likely to be?  What is the nature of the image?  ANSWER

Ray Diagrams in Converging Lenses

We can determine where an image lies in relation to the objects by using a ray diagram.  We can do this by using two simple rules:

• Draw a ray from the top of the image parallel to the principal axis.  This ray bends at the lens axis and goes through the principal focus.

• Draw a ray from the top of the lens through the centre of the lens.

Where the two rays meet, that is where the image is found.  The diagrams shows how we do a ray diagram step-by-step:

Step 1  Draw the ray parallel to the principal axis.

Step 2  Draw the refracted ray so that it passes through the principal focus.

Step 3 Draw a ray from the top of the object through the middle of the lens.  This ray is undeviated.

Step 4 Where the rays meet, that is where the image is.

It is a good idea to draw your ray diagrams on graph paper as the following ray diagrams are.  Be careful with your drawing; a small change in the angle of the undeviated ray can lead to quite a big change in the final position of the image.  And PLEASE... Be a good chap and use a sharp pencil.

Question 8  Draw a ray diagram to show the position of the image on a film where the object distance is three times the focal length of the camera lens.  What is the nature of the image?  ANSWER.

Diverging Lens

The diverging (concave) lens makes the rays split apart or diverge, as shown in the picture.

Note how the diverging rays are extended back, and come together at the principal focus.  The image of a diverging lens is virtual.

Correcting Eyesight

Short sight is usually caused by the converging lens in the eye being too strong, which means it brings the rays together in front of the retina, so that the image on the retina is not focused properly, and is blurred.

Diverging lenses are used in glasses that correct short sight. 

Converging lenses are used to correct long sight, where people cannot make the lens fat enough to see close-up objects clearly.

The converging lens brings the rays in so that the image is focused correctly on the retina.

Answer Question 9 which gets you to match up definitions used in lenses.

Have a go at the Crossword that gets you to think about mirrors and lenses.

Now try the Topic Quiz

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