Method for Finding the Focal Length in a Mirror

Concept sheet | Physics
Important!

This concept sheet explains the steps to follow to find the focal length in a mirror.

The focal length is the distance between the top of the mirror and the focal point, that is, the point where all the reflected rays intersect (in a converging mirror), or the point where all the extensions of reflected rays intersect (in a diverging mirror).

The focal length can be measured in different mirrors.

Focal Length in a Converging Cylindrical Mirror

Equipment

  • Ray box

  • Converging cylindrical mirror

  • Sheet of paper

  • Ruler

  • Pencil

Equipment

Procedure

1. Place the mirror in front of the ray box on the sheet of paper.

Procedure

2. Using a pencil, draw a line along the mirror tracing its reflecting surface on the sheet of paper.

Procedure

3. Light the ray box and send three rays of light into the mirror so that the incident and reflected rays from the centre overlap.

Procedure

4. Using the pencil, note where the reflected rays intersect, while observing the reflection of the rays.

Procedure

5. Remove the mirror and the ray box from the sheet of paper.

6. Measure the distance from the top of the mirror to the focal point. This distance represents the focal length of the mirror.

Procedure
Procedure

7. Put away the equipment.

Results

By knowing the position of the focus, it is possible to determine the focal length of the mirror used. Simply measure the distance between the tip of the mirror and the focal point. In the example above, the focal length of the mirror is |2.5\ \text {cm}|.

Focal Length in a Diverging Cylindrical Mirror

Equipment

  • Ray box

  • Diverging cylindrical mirror

  • Sheet of paper

  • Ruler

  • Pencil

Procedure

Procedure

1. Place the mirror in front of the ray box on the sheet of paper.

Procedure

2. Using a pencil, draw a line along the mirror tracing its reflective surface on the sheet of paper.

Procedure

3. Turn on the ray box and send three rays of light to the mirror so that the incident and reflected rays from the centre overlap.

Procedure

4. Use dotted lines to draw the rays reflected by the convex mirror.

Procedure

5. Remove the mirror and the ray box from the sheet of paper.

6. Extend the reflected rays from the opposite side of the mirror.

 

Procedure

7. Using a pencil, note where the reflected rays meet. This point is the focal point.

Procedure

8. Measure the distance between the top of the mirror and the focal point. This figure represents the focal length of the mirror.

Procedure
Procedure

9. Put the equipment away.

Results

By knowing the position of the focus, it is possible to determine the focal length of the mirror used. Simply measure the distance between the top of the mirror and the focal point. In the example above, the focal length of the mirror is |2.6\ \text {cm}|.

Focal length in a converging spherical mirror

Equipment

  • Optical bench

  • Light source

  • Converging spherical mirror

  • Mirror support

  • Screen

  • Screen support

Equipment

Procedure

1.​​ Assemble the optical bench: place the metre stick into its supports.

Procedure

2. Place the spherical mirror in its support, and place it at one end of the optical bench.

Procedure
Important!

The position of the mirror support pointer indicates the position of the top of the mirror.

3. Place a light source at the other end of the optical bench, as far away from the mirror as possible.

Procedure

4. Place the screen in the screen support, and position the support so that it can catch the rays reflected by the mirror. If necessary, rotate the mirror.

Procedure
Be careful!

It is preferable to place the light source and the screen on either side of the optical bench.

5. Move the screen until the captured image is in focus, that is, the image is clear, crisp, bright, and small.

Procedure

6. Using the tape measure, measure the distance between the focal point (screen position) and the top (mirror position). This distance represents the focal length of the mirror.

Procedure

7. Put away the equipment.

Results

In the example above, the distance between the screen position and the mirror is |5.9\ \text {cm}|.

Important!

Because the centre of curvature in mirrors is at a distance that is twice the focal length, it is possible to determine the radius of curvature by multiplying the result obtained by 2.