Triple Physics Topic 3 - Refraction and Lenses

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 1 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)?

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 2 How does the path of the emergent ray compare with the path of the undeviated ray?

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.  The formation of the spectrum is a result of dispersion of white light.

Refractive index

When light passes from air into glass, it slows down from 3 × 108 m/s to about 2 × 108 m/s.  The refractive index is the ratio of the speed of light in air to the speed of light in the glass, which we can write as:

refractive index = speed of light in air ÷ speed of light in glass.

Refractive index has no units; it's just a number.

 What is the refractive index of the glass in the example above?

If we increase the angle of incidence, we find that the angle of refraction increases as well.  But it's not a simple relationship.  For example, suppose the angle of incidence is 20o and the angle of refraction is 15o.  Double the angle of incidence to 40o, and the angle of refraction is NOT 30o, but 29o.  The relationship is:

refractive index = sin i

sin r

 Question 4 The angle of incidence is 20o and the angle of refraction is 15o.  What is the refractive index of the material?

Make sure your calculator is set to degrees.

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.

In the exam, the following notation for a lens will be used:

AQA syllabus

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:

 Object at Image at Size Orientation Nature Use Infinity F Diminished Inverted Real Image on a film (at infinity) >2F Between F and 2F Diminished Inverted Real Image on a film (close up) 2F 2F Same size Inverted Real Photocopier Between 2F and F >2F Magnified Inverted Real Projector F Infinity Magnified Inverted Real Spot light

A real image can be projected onto a screen.  A virtual image cannot be projected onto a screen.  Magnified means made bigger, while diminished means made smaller.  Inverted means turned upside down.

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

Know how to use this in the exam.  This formula will be given:

magnification = image height

object height

 Question 5 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?

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 diagram is.  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 6 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?

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.

Images of Convex Lenses

A real image can be projected onto a screen.

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

magnification = height of image

height of object

The ray diagram shows the object at a distance bigger than 2F (twice the focal length)

This one is at 2F:

This one is between F and 2F:

This one is at F:

 Question 7 Match the definitions used with lenses

 Question 8 Have a go at the Crossword that gets you to think about mirrors and lenses.

 Summary All angles are measured from the normal. The angle of incidence is equal to the angle of reflection. Image in a plane mirror is upright, laterally inverted and virtual Refraction occurs at an interface, e.g. between air and glass. Prisms refract light.  White light is split up into a spectrum. The image produced by a diverging lens is virtual. Images produced by converging lenses are usually real and inverted. A converging lens used as a magnifying glass produces an upright, magnified, and virtual image. Converging lenses are used in many optical devices. Converging and diverging lenses are used to correct defects of vision.