# Spherometer Experiment

**Spherometer Experiment for Class 11 ****with Readings**

**Aim**

i. To find the thickness of a glass piece (glass strip).

ii. To find the radius of curvature of a spherical surface.

**Apparatus **

Spherometer, large glass sheet. glass strip, spherical surface etc.

**Principle **

Thickness of a glass strip, h = n x pitch + X x LC. -------------- (1)

Where, n = no. of complete rotations.

X = no. of additional circular scale (head scale) divisions which are in excess of the complete rotations. (fractional rotations).

LC = least count = pitch/no. of h.s.d.

Radius of curvature of the spherical surface is,

where, h — height of the central screw above the plane glass surface.

a — perpendicular distance between one of the (three) legs of the spherometer and the vertical line through the central screw.

l — distance between any two legs.

**Procedure **

**i. To find the least count (LC) **

First zero of the head scale is brought in line with a
division on the vertical scale (pitch scale). The screw is then rotated, for,
say N_{o} = 5 complete rotations and the distance 'y' moved by the
screw along the pitch scale is noted. Then the pitch is,

p = y/N_{o} = mm and LC = pitch/no of h.s.d = P/N
mm,

**ii. To find the thickness of the glass strip. **

Spherometer is placed on the large glass sheet, so that its three legs rest on the plane glass surface. The central screw is raised sufficiently by rotating it. The given glass strip is now introduced between the central screw and the plane glass sheet. The central screw is then rotated slowly downwards till its tip just touches the glass strip. The head scale reading which is in line with the pitch scale is noted. The glass strip is then gently removed and the central screw is rotated downwards till its tip just touches the plane glass sheet. The number of complete rotations (n) with reference to the initial head scale reading and fractional rotations (X) are noted. The thickness of the glass strip is found out using the relation (1). The experiment is repeated.

**iii. To find the radius of curvature of a spherical surface **

**a. Convex surface **

The convex surface is placed on the plane glass sheet. Then the spherometer is placed over the convex surface so that its three legs rest on the convex surface. The central screw is rotated slowly, downwards till its tip just touches the convex surface. The head scale reading coinciding with the pitch scale is noted. The spherometer and the convex surface are removed. The spherometer is now placed on the plane glass sheet and the central screw is slowly rotated downwards till its tip just touches the plane glass sheet. The number of complete rotations (n) and the number of fractional rotations (X) are noted. The distance, h, moved by the central screw is found out using the relation (1).

The central screw is raised and the spherometer is placed on the note book, so as to get the pricks of the three legs on the paper. The three pricks are marked as A, B and C. These three points are joined to form a triangle (equilateral triangle). The sides AB, BC and CA are measured and the mean length 'I' is noted. Then the radius of curvature of the convex spherical surface is found out using relation (2). Experiment is repeated.

**b. Concave surface **

In this case the spherometer is first placed on the plane glass sheet and the head scale reading is taken. Then it is placed on the concave surface. The same procedure is followed to find h and R as for the convex surface.

**Observations and Readings**

**(a) To find the thickness of the glass plate**

Distance moved by the screw for 10 complete rotations = __10
mm__

Therefore, Pitch of the screw = __1 mm__

Number of divisions of the head scale = __100__

Therefore, Least count = __.01 mm__

Mean thickness = __1.92 mm__ = __1.92 x 10__^{-3}m

**(b) To find the radius of curvature of the spherical surface**

Distance between any two legs (l) = __3.2 cms__

R = l^{2}/6h + h/2 = __7.54 cms__ = __7.54 x 10__^{-2}m

**Results **

i. Thickness of glass strip = __1.92 x 10__^{-3}m

ii. Radius of curvature of spherical surface = __7.54 x 10__^{-2}m

**MODEL VIVA VOCE QUESTIONS AND ANSWERS**

*1. What is the principle of a spherometer? *

Principle of micrometer screw.

*2. Mention the uses of a spherometer.*

a. To measure the thickness of small glass pieces

b. To find the radius of curvature of spherical surfaces.

*3. Why is spherometer called
so? *

Since it is used to measure the radius of curvature of spherical surfaces, it is named as spherometer.

*4. Mention the precautions to be taken. *

a. The parallax should be removed tip to tip.

b. The head screw should always be turned in the direction only while taking reading to avoid back-lash error.

*5. What are the sources of error? *

a. The parallax may not be removed tip to tip.

b. The apparatus may have back-lash error.

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