# Spherometer Experiment

Experiment: Determine the radius of curvature of a concave mirror using a spherometer.

### Spherometer

When a spherometer is placed on a curved surface such that all its legs are touching it, the middle leg will be a little higher or lower than the plane of the outer legs by a small amount h which is related to R, the radius of curvature of the surface. GH = h

GOE = 2R

AH = a, the distance between the central leg and the outer leg.

From geometry,

AH × HB = GH × HE

a × a = h (2R – h)

a2 = 2Rh – h2

2RH = a2 + h2

R = a2/2h + h2/2h

R = a2/2h + h/2

H is the centre of equilateral triangle formed by the outer legs A, B, C.

cos 30° = AM/AH

√3/2 = l/2a

a = l/√3

R = l2/6h + h/2

Material Required

Spherometer, plane glass slab, concave mirror, half metre rod

### How To Perform the Experiment

1. Examine the spherometer, noting carefully that the legs and the vertical scale are not shaky and that the central screw is not very loose.

2. Find the pitch of the screw by determining the vertical distance covered in 4 or 5 rotations.

Pitch = Distance moved / No. of complete rotations

3. Find the least count by dividing the pitch by number of divisions on the circular scale.

Least count = Pitch of the screw / No. of divisions on circular scale

4. Set the given concave mirror on a horizontal surface firmly and place the spherometer on it and adjust the central leg till it touches the surface. All the four legs touch the surface of the concave mirror.

5. In order to eliminate back-lash error, proceed slowly as the central leg reach close to the mirror surface. Stop when central leg touches the mirror surface and
the entire spherometer just rotates, hanging on the central leg.

6. Read the coincident division on the circular scale and also the main scale reading on the vertical scale. Thus find the total reading.

7. Now place the instrument on the surface of the plane glass slab and find how many complete turns have to be made to bring the tip of the central leg to the plane of the outer leg. Also read the coincident division on the circular scale. Thus find the total reading on the glass slab. The difference between the above two readings gives h.

8. Press the spherometer gently on the notebook so as to get pricks of the feet which are pointed. Measure the distance between each pair of outer pricks and find their mean. This gives l.

### Sources of Errors

1. By spherometer we find R of front surface of the mirror. But its back surface is polished.
2. Since l is very small, an error in it causes large percentage error in the result.
3. Back-lash error is eliminated only by the weight of the spherometer. Since it is a small weight, back-lash error may be only partially eliminated by it.