Class 12 Physics Practical – Finding the Focal Length of a Concave Mirror

Aim

To find the value of v for different values of u in case of a concave mirror and to determine its focal length.

Apparatus Required

Optical bench, three uprights with lateral adjustment, concave mirror, mirror holder, two pins, a knitting needle, and a half-metre scale.

Theory

The focal length f of a concave mirror is related to object distance u and image distance v using the mirror formula:

1/f = 1/u + 1/v

f = uv/(u+v)

Using the Cartesian sign convention,

• u, v, and f are negative for concave mirrors.

Ray Diagram

Procedure

1. Determine the approximate focal length by projecting the image of a distant object onto a wall using the concave mirror.
2. Place the concave mirror on the optical bench along with the uprights and ensure the needles face the mirror.
3. Adjust the bench screws so the mirror is perfectly vertical and its principal axis is parallel to the bench scale.
4. Record the index mark of the mirror upright.
   Place the object pin so that the tip and pole lie horizontally aligned and separated by a length equal to the knitting needle (x cm).
   Record the object pin position (y cm).
   Index correction for u = (x − y) cm.
5. Repeat the same method to find index correction for the image distance v.
6. Place the object pin at ~1.5 times the approximate focal length.
   Adjust the height so the needle is level with the mirror’s pole.
   You should see an enlarged, inverted image.
7. Place the image pin beyond twice the approximate focal length.
   Align its height and use the lateral motion screws to make the tips coincide.
8. Move your eye sideways to check for parallax.
   Adjust until no parallax is seen — the tips should overlap from all viewpoints.
9. Record the scale readings for mirror, object pin, and image pin.
10. Repeat for at least five different object distances (shift object pin by ~2 cm each time).

Observations

Precautions

1. The pole of the mirror and needle tips must be at the same height.
2. All uprights must be perfectly vertical.
3. Parallax must be completely removed.
4. Index corrections must be properly applied.
5. Keep the observing eye at least 30 cm from the image needle.

Sources of Error

1. Needle tips and pole not at same height.
2. Incorrect index correction.
3. Parallax not properly removed.