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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.

Convex mirror with principle axis, focal point (F) and centre of curvature (C). The centre of the mirror is the optical centre (O).

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] .

A convex mirror with three rays drawn to locate the image. Each incident ray is reflected according to the Law of Reflection. The reflected rays diverge. If the reflected rays are extended behind the mirror, then their intersection gives the location of the image behind the mirror. For a convex mirror, the image is virtual and upright.

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] .

Summary of properties of concave and convex mirrors.
Plane Concave Convex
converging diverging
virtual image real image virtual image
upright inverted upright
image behind mirror image in front of mirror image behind mirror

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 .

m = h i h o

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 = 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 .

A concave mirror forms an image that is 4,8 cm high. The height of the object is 1,6 cm. Calculate the magnification of the mirror.

  1. Image height h i = 4,8 cm

    Object height h o = 1,6 cm

    Magnification m = ?

  2. m = h i h o = 4 , 8 1 , 6 = 3

    The magnification is 3 times.

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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?

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Source:  OpenStax, Siyavula textbooks: grade 10 physical science. OpenStax CNX. Aug 29, 2011 Download for free at http://cnx.org/content/col11245/1.3
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