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Spherometer Aim: To measure the radius of curvature of a given spherical surface by using a
spherometer. Apparatus : A spherometer, a plane glass plate and a spherical surface. Theory:
CB represents the distance ‘h’ through which the screw tip (centre leg in diagram) should be lowered lowered so that it may just touch the plane surface. surface. AB is the distance distance between between one of the legs and the screw when they are resting on a plane surface. If ‘R’ be the radius of curvature, OD
2
= BD 2 + OB 2
OD
2
= BD 2 + (OC − BC ) 2
R
2
= a 2 + ( R − h) 2
R
2
= a 2 + R 2 − 2 Rh + h 2
2 Rh = a 2 + h 2 R
=
a
2
+
h
2h 2 The 3 outer legs of a spherometer form an equilateral triangle. The screw tip equidistant from each leg at distance a, is at the centroid of the triangle. If ‘l ’ is the distance between any two legs, then, ‘a’ = l /√3 Substituting for a in the equation
R
=
2
l
6h
+
h
2
: 1. Determine the pitch and the least count of spherometer. 2. Place the plano convex lens in such a way that its convex surface is the upper most. 3. Take the spherometer and place it on the convex surface of the lens. Adjust the screw in such a way that its tip just touches the spherical surface. Note and record the number of the division on the circular scale which lies in line with the pitch scale. 4. Remove the convex mirror from its position and let the three legs of the spherometer rest on the plane glass plate, without disturbing the screw position. 5. Now turn very gently in the clockwise direction and lower down the screw till its tip just touches the surface of the glass plate. While lowering down the screw, count the number of
Procedure
complete rotations made by the disc, taking the initial reading of the circular scale as the reference point. Also note the number of the division of the circular scale which lies in line with the main scale. 6. Repeat steps 2,3,4 and 5 four times more by placing the instrument at different positions on the spherical surface and record the observations. 7. Place the spherometer on a clean page and press the knob of the spherometer screw a little hard so that the impressions of all the tips of its three legs are obtained on the paper. Mark them as A, B and C. 8. Join the dots with the help of a sharp pencil and measure the distance between the dots with a millimetre scale and take the mean of these three distances as l . Observations:
Pitch = distance moved on the linear scale = …………………… mm no. of rotations L.C =
Pitch = ……………….. mm No. of div on circular scale
Distance between legs of the spherometer, l =i……, ii……, iii……, mean……….. To measure the sagitta , h Obs no. No. of complete rotations m
R=
2
l
6h
+
Circular scale reading
Fractional h= (m x pitch) rotation + (n x L.C) On curved On the flat n = (a-b) or surface (a) surface (b) (100+a-b)
h
2
R = ……………. mm 2
∆h l ∆h ∆l Error calculation= ∆ R = (2 ) + ( ) + 2 h 6h l
=………………..mm Result: R = ……………… ± ……………….. mm PRECAUTIONS 1. Examine the working of the spherometer before starting the experiment and make sure that the main scale and the legs are not shaky and the screw turns smoothly. 2. The size of the spherical surface should be large enough so that all the legs of the spherometer can rest on it simultaneously.
3. The screw should always be turned in the same direction to avoid back lash error. 4. The screw head should be turned gently and the proper ‘just touch’ position of the screw tip with the surface should be ascertained. 5. The impressions of the tips of the legs on the practical note book should be taken carefully and the pricks should be circled and joined immediately after removing the spherometer. 6. A small error in the measurement of ‘l’ will result in a large error in the result. So, it should be measured as accurately as possible. SOURCES OF ERROR 1. The judgement of the proper touch of the screw tip with the surface may not be very accurate inspite of the best efforts. 2. The screw may not have threads accurately cut and as a result of it, the pitch may not be constant at different places on the screw. 3. The graduations on the circular and pitch scales may not be uniform. 4. The spherometer may have back lash error. 5. The screw may have friction.
