13.3 Mirrors

Convergence

A concave mirror is also known as a converging mirror. Light rays appear to converge to the focal point of a concave mirror.

Convex mirrors

The second type of curved mirror we will study are convex mirrors. Convex mirrors have the shape shown in [link] . As with a plane mirror, the principal axis is a line that is perpendicular to the centre of the mirror.

We have defined the focal point as that point that is half-way along the principal axis between the centre of curvature and the mirror. Now for a convex mirror, this point is behind the mirror. A convex mirror has a negative focal length because the focal point is behind the mirror.

To determine what the image from a convex mirror looks like and where the image is located, we need to remember that a mirror obeys the laws of reflection and that light appears to come from the image. The image created by a convex mirror is shown in [link] .

From [link] , we see that the image created by a convex mirror is virtual and upright, as compared to the real and inverted image created by a concave mirror.

Divergence

A convex mirror is also known as a diverging mirror. Light rays appear to diverge from the focal point of a convex mirror.

Summary of properties of mirrors

The properties of mirrors are summarised in [link] .

Magnification

In  [link] and [link] , the height of the object and image arrows were different. In any optical system where images are formed from objects, the ratio of the image height, $h_i$ , to the object height, $h_o$ is known as the magnification, $m$ .

This is true for the mirror examples we showed above and will also be true for lenses, which will be introduced in the next sections. For a plane mirror, the height of the image is the same as the height of the object, so the magnification is simply $m=\frac{h_i}{h_o}=1$ . If the magnification is greater than 1, the image is larger than the object and is said to be magnified . If the magnification is less than 1, the image is smaller than the object so the image is said to be diminished .

Mirrors

1. List 5 properties of a virtual image created by reflection from a plane mirror.
   
2. What angle does the principal axis make with a plane mirror?
   
3. Is the principal axis a normal to the surface of the plane mirror?
   
4. Do the reflected rays that contribute to forming the image from a plane mirror obey the law of reflection?
   
5. If a candle is placed 50 cm in front of a plane mirror, how far behind the plane mirror will the image be? Draw a ray diagram to show how the image is formed.
   
6. If a stool 0,5 m high is placed 2 m in front of a plane mirror, how far behind the plane mirror will the image be and how high will the image be?
   
7. If Susan stands 3 m in front of a plane mirror, how far from Susan will her image be located?
   
8. Explain why ambulances have the word `ambulance' reversed on the front bonnet of the car?
   
9. Complete the diagram by filling in the missing lines to locate the image.

   

10. An object 2 cm high is placed 4 cm in front of a plane mirror. Draw a ray diagram, showing the object, the mirror and the position of the image.
    
11. The image of an object is located 5 cm behind a plane mirror. Draw a ray diagram, showing the image, the mirror and the position of the object.
    
12. How high must a mirror be so that you can see your whole body in it? Does it make a difference if you change the distance you stand in front of the mirror? Explain.
    
13. If 1-year old Tommy crawls towards a mirror at a rate of 0,3 m $·$ s ${}^{-1}$ , at what speed will Tommy and his image approach each other?
    
14. Use a diagram to explain how light converges to the focal point of a concave mirror.
    
15. Use a diagram to explain how light diverges away from the focal point of a convex mirror.
    
16. An object 1 cm high is placed 4 cm from a concave mirror. If the focal length of the mirror is 2 cm, find the position and size of the image by means of a ray diagram. Is the image real or virtual? What is the magnification?
    
17. An object 2 cm high is placed 4 cm from a convex mirror. If the focal length of the mirror is 4 cm, find the position and size of the image by means of a ray diagram. Is the image real or virtual? What is the magnification?