To determine the focal length of a concave mirror by obtaining image of a distant object.

Aim

To determine the feral length of a concave mirror by obtaining image of a distant object.

Materials and Apparatus Required

A concave mirror, a metre scale, a small screen fixed on a stand and a mirror holder.

Theory

A spherical surface which is silvered or brightly polished so as to reflect light incident on its concave side is called concave mirror. The centre of the sphere of which the mirror is a part is called the centre of curvature. The central point P of the spherical surface of the mirror is called the pole of the mirror. The line joining the pole to the centre of curvature C is called the principal axis. The radius of the sphere of which the surface of the mirror forms a part is called the radius of curvature of the mirror.

The incident rays parallel to principal axis on a concave mirror, after reflection meet at a point on the principal axis. This point is called the principal focus or simply focus. It is denoted by F. A plane passing through the focus and normal to principal axis is called focal plane. The distance of focus from the pole of mirror is called focal length of the mirror. It is denoted by f.

The focal length of a concave mirror is given by:
1 / Focal length = (1 / Image distance) + (1 / Object distance)

i.e. ( 1 / f) = (1 / v) + (1 / u)

or

f = uv / (u = v)

where,
v = distance of image from mirror
u = distance of object from mirror
f = focal length of the mirror

When the object is at infinity in front of a concave mirror, its image is formed at the focus of the mirror.

A distant object (a tree or a distant building or an electricity pole) can be considered as an object at infinity, and its image will be formed at the focus of the mirror. The image formed is real, inverted and very small in size.

Since the image formed by the mirror is real, it can be obtained on the screen. Thus, we can estimate the focal of a concave mirror by obtaining a real image of a distant object at its focus.

Procedure

1. Hold the given concave mirror with the help of its stand without obstructing its aperture.
2. Face the mirror towards the window of your laboratory from which a distant object like a tree is visible.
3. Place the screen in front of the concave mirror.
4. Select the right position of the screen by moving it back and forth so that a sharp, clear and inverted image of the distant tree is formed on it. We can get a clear and bright image if the distant object is illuminated with sunlight and the screen is placed in the shade. We can also get an image of the sun if sunlight is made to fall directly on the concave mirror.
5. Now, mark the position of the centre of the stands holding the mirror and the screen.
6. Measure the horizontal distance between the concave mirror and the screen using a metre scale.
7. Note the observations in the observation table.
8. Repeat the experiment two more times by obtaining the image of two different distant objects. Measure the distances between the concave mirror and the screen in each case.
9. Record the observations in table.
10. Calculate the mean value of the focal length.

Observations

Calculation

Mean focal length f = (f1 + f2 + f3 / 3) cm.

Result

The approximate focal length of the given concave mirror is .............. cm.

Precautions

1. The distant object taken for seeing the image should be clearly visible.
2. Image obtained on the screen should be sharp and distinct.
3. Mirror surface should be clean.
4. No obstacle should be in the path of rays of light from the distant object, incident on the concave mirror.
5. Sunlight should never be focussed with a concave mirror on the sheet of paper. The heat produced due to the concentration of sunlight ignites the paper. The image of the sun should be focussed only on the screen.