To find the focal point and the

centre of curvature of concave

mirror, to determine the

relationship between the radius of

curvature and the focal length of

this mirror.

The radius of curvature

should be twice the focal

length.

Concave mirror

Ray box

Blank sheet of paper

ruler

1) Draw a straight horizontal line passing through the middle of the

paper to represent the principal axis.

2) Set up the apparatus as shown in the diagram below.

Principal axis

Ray box

Concave Mirror

3) Trace the outline of the concave mirror

4) Darken the room and adjust the ray box so that the five light

rays are parallel to each other and the principal axis.

5) Trace the incident and reflected rays.

6) Mark the intersection point of the reflected rays. This is the

focal point (F) of the mirror. (Refer to figure 1 for further

explanation. )

7) Using a ruler, measure the distance from the focal point to the

vertex (V) of the concave mirror. This is known as the focal

length of the mirror.

8) Adjust the ray box from 5 slits to a single slit and direct it

towards the mirror. Adjust the direction of the single ray until the

reflected ray coincides with the incident ray. Repeat step 8 and

find the second ray.

The point where the two rays meet is the center of curvature (C)

of the mirror.

9) Using a ruler, measure the distance from the center of curvature

to the vertex of the concave mirror. This is known as the radius

of curvature.

20.61cm

v

Figure 1: Finding the Focal Point for a Concave Mirror

10.30cm

Figure 2: Finding the Center of Curvature for a Concave Mirror

20.61cm

Analysis of the results

Errors and improvements

Laws used in the lab

Analysis of the result1) According to the result Figure 1 and 2 the radius of curvature is

20.63 cm and the focal length is 10.30cm. It is obvious that the

radius of curvature is twice the focal length. According to the law of

reflection, the angle of incidence is equal to the angle of refraction:

O1=O2 . Since angles O1 and O3 are alternate interior angles,

O1=O3. So, O2=O3. Triangle ACF is therefore an isosceles

triangle. As a result, it has two equal sides: CF=AF. When the size

of mirror is smaller than the radius of curvature, angle CAV is equal

to 90 degrees, which means triangle CAV is a right triangle

therefore FA=FV. So, CF=FV.

C F

A

V

O1O2

O3

Thus, the focal point is located at the

half way point of segment CV. Since

VF is the focal length(f) and CV is the

radius of curvature(R), we can write:

f=R/2.

Errors and Improvement

2) In Figure 1, the 5 reflected rays do not

exactly intersect at the focal point but form

a shade on the principle axis and leads to

the inaccuracy of the measurement of focal

length. This is because the light beams are

not sharp enough. These errors can be

reduced by using sharper rays.

Laws used in the lab

3)We have previously established that the law of reflection can be applied to curved mirrors. If you look closely at the reflective surface of a spherical mirror. It is actually linear. A single ray of light striking the mirror, only hits a small portion of mirror. if each sector is thought as being plane, than Snell’s law of reflection can be obeyed on curved mirrors as well.

What happened in the experiment.

What does the data tell you about you experiment

Application of concave mirror

What did you learn

In this lab, the focal length was determined by directing

5 parallel rays towards the concave mirror. The radius of

curvature was determined to be twice the focal length

of the concave mirror using the ray box and the other

equipments provided. As mentioned previously, the

focal length is approximately 10.30cm according to

Figure 1 and the radius of curvature is approximately

20.61cm according to Figure 2.

Concave mirrors can serve a wide variety of purposes

in reality. They are used in cosmetics to enlarge areas

of the face when applying make-up.

They are also used as dentists' mirrors to magnify the

image of a patients teeth to facilitate the

examination.  It has been learned from this lab the

relationship between the radius of curvature and the

focal length of a concave mirror is always 2:1.