Keywords

• Centre of curvature.
• Focal point
• Principal focus
• Pole

By the end of this chapter, you will be able to:

• Understand reflection of light and the formation of images by curved mirrors.
• Use ray diagrams to show how images are formed by curved mirrors and the nature of the images.
• Determine the focal length of concave mirrors using a variety of methods.

Introduction

Have you ever thought about what it would be like to live without light? Or maybe what happens at night in a lit room and all of a sudden light goes out?

 You may also have wondered how you look when you stand before different types of mirrors etc. In this chapter, you will understand how concave and convex mirrors form images. You will also be able to describe the use of these mirrors in everyday life.

Activity 5.1 Describing curved mirrors Reflection of Light by Curved Surfaces

What you need

• A silver teaspoon, a pen.

 What to do

1. Get a teaspoon and observe yourself in it.
2. Describe your image as seen on the spoon
3. Bring a pen close to the spoon and observe the image formed. Move the pen slowly away from the spoon.
4. Compare your discoveries in (a) and (c) above
5. Now change the other side of the spoon and observe yourself in the spoon.
6. Bring a pen close to the spoon and observe the image formed.
7. Move the pen slowly away from the spoon. Describe the changes in the image in the spoon.
8. Compare your discoveries in (f) and (g) above.
9. By use of ray diagrams, determine the position, size and nature of the image of an object 4cm tall placed on the principal axis of a concave mirror of focal length 15cm at a distance 30cm from the mirror

 In part (a) of Activity 5.1, you were looking at yourself from the outer surface of the spoon. In this case, the spoon was used as a convex mirror. While in part (f), you were looking at yourself from the inner surface of the spoon. In this case the spoon was used as a concave mirror.

With reference to the above statements:

 (i) How many types of curved mirrors are there? Identify them.

(ii) Describe how each of these curved mirrors is formed.

TERMS USED IN CURVED MIRRORS

Figure 5.1: Concave and convex mirrors respectively

Curved mirrors are parts of a sphere. The following terms are used in curved mirrors:

• Pole P – it is the centre of the mirror.
• Centre of curvature C– it is the centre of the sphere of which the mirror is part.
• Radius of curvature r– it is the radius of the sphere of which the mirror is part.
• Principal axis – it is a line drawn through the pole of the mirror and the centre of curvature.
• Principal focus F – for a concave mirror, it is the point at which all rays parallel and close to the principal axis converge after reflection. In the case of a convex mirror, it is the point from which all rays parallel and close to the principal axis appears to diverge after reflection (see the figure above). It is also called the focal point.
• Focal length f – it is the distance between the pole of the mirror and its focal point.

When rays are extended behind the mirror, they are indicated using dotted lines. This means that they are imaginary or virtual. Hence, the focal point and focal length of a concave mirror are real while the focal point and focal length of a convex mirror are virtual. A real focal length is given a positive sign while a negative focal length is given a negative sign.

Image formation in curved mirrors

This is governed by drawing the following rules:

• Any incident ray travelling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection.
• Any incident ray passing through the centre of curvature on upon reflection. The way to the mirror will travel back along its incident path

This is summarized in the figure below:

Figure 5.2: Image formation by a spherical mirror

F is the focal point of the concave mirror.

Summary of steps taken to locate an image formed by a concave mirror

• Step One: Draw a ray, starting from the top of the object parallel to the principal axis and then through the focal point after reflection
• Step Two: Draw a ray, starting from the top of the object through the focal point, then parallel to the principal axis after reflection
• Step Three: Draw a ray, starting from the top of the object, Then back upon itself
• Step Four: After getting the intersection, draw an image from the principal axis to the point of intersection.

Activity 5.2 forming an image by a concave mirror

Key Question: How can you locate an image formed by a concave mirror?

What to do

• Starting with Figure 5.3, construct the ray diagram and locate the final image formed by a concave mirror

Figure 5.3: Formation of an image by a concave mirror

1. State the characteristics of the image formed in Figure 5.3.
2. Construct a ray diagram to locate the image when the object is;
3. At C
4. Between C and F
5. At F
6. Between F and P

In each case, summarize the characteristics of the image. What do you notice as the object is moved towards the mirror?

• Compare your findings with the observations you made in Activity 5.1 (i).

Activity 5.3 forming an image by a convex mirror

Key Question: How can you locate an image formed by a convex mirror?

What to do

Starting with the figure provided, follow all the steps summarized above to locate the final image formed by a convex mirror.

Figure 5.4: Formation of an image by a convex mirror

a) State the characteristics of the image formed in Figure 5.4

 (b) Construct ray diagrams to locate the image when the object is placed at different distances in front of the convex mirror.

In each case, summarize the characteristics of the image. What do you notice?

(c) Compare your findings with the observations you made in Activity 5.1 (i).

Construction of ray diagrams using scale drawing

Scale drawing

At times you find that the distance between the object and the mirror is too long and cannot fit in your note book. For example, cannot fit in you if the distance between the object and the mirror is 120cm, this note book if you are to draw a ray diagram to locate the position of the image. In such a case, it is more convenient to choose an appropriate scale for your drawing.

For example

1cm: 10cm

12cm: 120cm

Now, instead of drawing 120cm you only draw 12cm, which can fit properly in your notebook.

Note:

1. once you choose a scale, it must be applied to the whole drawing in the figure.

2. To report the final distances and heights, use the scale to find the actual values of these distances and heights.

Exercise 5.1

 Use scale drawings to locate the position and size of the image if:

 (a) an object of height 8cm is placed 24cm in front of a concave mirror of focal length 12cm is again placed  in front of a concave mirror of focal length 15cm.

 (b) An object of height 12cm is placed 9cm in front of a concave mirror of focal length 15cm.

(c) an object of height 10cm is placed 20cm in front of a convex mirror of focal length 12cm.

Determination of focal length of concave mirrors

 Method 1: Using two pins

Activity 5.4 finding the focal length of concave mirror using two pin method

Key Question: By use of two pins, describe an experiment you would perform in a laboratory to determine the focal length of a concave mirror.

What you need

• Concave mirror, optical bench, object and image pins, metre rule. Arrange your set – up as indicated below:

Figure 5.5. Arrangement of apparatus to determine focal length of a concave mirror

What to do

 1. Place pin 0 at a distance U 16cm in front of the concave mirror.

 2. Move pin I in front of the mirror to locate a point where there is no parallax between the image of 0 as seen in the mirror and I

3. Measure and record the distance, V, between I and M.

4. Repeat procedures (1) to (3) for U = 18, 20, 22 and 24cm.

5. Record your results in a suitable table including the values of UV and (U + V).

6. Plot a graph of UV against (U + V).

7. Find the slope of your graph.

8. Explain the physical meaning of your slope.

 Method II: Distant object

Activity 5.5 Determinating focal length of concave mirror using a distant object

 What you need

• Metre rule, concave mirror, table or any flat surface and a screen.

 What to do

Arrange your apparatus as shown in Figure 5.6

Figure 5.6 determining the focal length of a concave mirror

1. Focus the image of a distant object on a screen using the concave mirror as shown in Figure 5.6.
2. Adjust the position of the screen until the image of the distant object is very clear on the screen.
3. Measure the distance between the screen and the mirror.
4. Comment on your result in (c) above.

Activity 5.6 Exploring uses of concave mirrors

 a) In groups, brainstorm and discuss different applications of concave mirrors. For a given point, use relevant examples.

b) Discuss your answers with the rest of class members.

Activity 5.7 Using curved mirrors

1. In groups, discuss the uses of convex mirrors.
2. Present your findings to the rest of the class.

Research 5.1

Key Question: By using different resources, discuss how curved mirrors are used in optical instruments and car headlamps.

What you need

• Internet, computers and any Physics textbook.

What to do

(a) In pairs, carry out an intensive research (using ray diagrams) on why curved mirrors are used in optical instruments like telescopes and car headlights.

(b) Write a report of your findings and present the findings to the whole class. You may note down important notes in your Physics notebook.

Chapter Summary

 In this chapter, you have learnt that:

• A concave mirror is a mirror that is silvered on the outer part of the curved surface.
• A convex mirror is a mirror that is silvered on the inner part of the curved surface.
• Focal length (f): The distance from the centre of the mirror to the focal point.
• The principal axis (P): A straight line drawn perpendicular to the plane of the mirror which passes through the mirror’s centre.
• The radius of curvature is the radius of the sphere from which the mirror was made

Image formation in spherical mirrors is defined by certain “characteristic “rays whose behavior