Determination of Focal Length of Concave Mirror and Convex Mirror

Let us understand a few terms before proceeding with the experiments-

Centre of curvature: The center of curvature for a curved mirror is defined as the center of a hollow glass sphere part of a curved mirror.
Radius of curvature: The radius of curvature is defined as the radius of the hollow glass sphere part of a spherical mirror.
Principal axis: Principal axis is the imaginary line that passes through the center of curvature and pole of the spherical mirror.
Principal focus: Principal focus is a point at which the reflected rays meet or appear to meet for the spherical mirror. The principal focus is in the front for a concave mirror, and for a convex mirror, the principal focus is behind the spherical mirror.

Experiment to determine the focal length of a concave mirror

Aim
To determine the focal length of:

Concave mirror
Convex lens by obtaining the image of a distant object.

Theory
We can obtain the focal length of a concave mirror in the following ways-

A concave mirror is a spherical mirror that reflects through a curved inner surface and follows the law of reflection of light.
The light rays coming from a distant object are considered to be parallel to each other.
The parallel rays of light meet the point in the front of the mirror if the image formed is real, inverted, and very small in size.
The image formed by the concave mirror is real and can be obtained on the screen.
f is used to denote the difference between the principal axis P and the focus F of the concave mirror.

We cannot obtain the focal length of the convex mirror directly as it forms virtual, erect, and diminished images. Instead, we will use an indirect method. Using a convex lens on the concave mirror and using the same techniques with some minor changes, we can find the focal length of a convex mirror. Those changes are-
1. Use a convex lens instead of a convex mirror.
2. The image will be formed behind the screen.
3. The image formed on the screen will be an inverted image.

We can obtain the focal length of a convex lens in the following ways-

The convex lens is thicker in the middle and thinner at the edges. It is also known as a converging lens.
The refracted rays from the parallel beam of light converge on the other side of the convex lens.
If the image is obtained at the lens's focus, the image is real, inverted, and very small.
f is the focal length which is the difference between the optical center of the lens and the principal focus.
The image formed is real and can be obtained on the screen.

To determine the focal length of a concave mirror

Materials Required
1. A concave mirror
2. A measuring scale
3. A screen holder
4. A mirror holder
5. A mirror stand

Procedure

1. Place the mirror at a distance of 60ft from the object.
2. Both the concave mirror and the object must face each other.
3. The screen must be placed in front of the mirror. Make sure the reflecting surface is in front to form the image. Adjust the screen accordingly to get a sharp and clear image of the object.
4. Use a ruler or metric scale to measure the distance between the concave mirror and the screen. This distance is the focal length of the given concave mirror.
5. Repeat the steps to get an average of the focal length for better results.

Observation table

S. no.	Position of a concave mirror (M)	Position of the screen (S)	Focal length (M-S)
1	70 cm	60 cm	10 cm
2	70 cm	60 cm	10 cm
3	70 cm	60 cm	10 cm

Calculation

Let us calculate the mean of the value of the focal length for better results-
(f1 + f2 + f3) / 3 = (10 + 10 + 10) / 3 = 10cm

Result

10 cm is the focal length of the concave mirror.

Precautions

1. Put the mirror and object in a well-illuminated area.
2. Place the concave mirror near the window to get a sharp image.
3. The polished mirror surface must face the object.
4. There should be no hurdle between the mirror and the object.
5. The mirror holder must be perpendicular to the measuring scale.
6. The mirror and screen must be parallel to the measuring scale.