Step-by-Step Spherometer Experiment Procedure and Calculations
We can define a spherometer as a measuring device which has a metallic triangular frame supported on three legs. The tips of these three legs form a triangle that is equilateral and which lie on the radius. In this article we will discover more things about the radius of curvature. There is a leg which is the central leg which can be moved in a direction which is perpendicular. In the below article there is the experiment on how to determine the radius of curvature of a given spherical surface by a spherometer.
To Determine Radius of Curvature of Spherical Surface
Aim of the Experiment:
To determine radius of curvature of a given spherical surface by a spherometer.
Apparatus:
a Spherometer for experiment, a convex surface (it may be an unpolished mirror), a big size plane glass slab or mirror which is plain.
Theory of Experiment:
The figure which is shown below is a schematic diagram of a single disk spherometer. It generally consists of a central legs which can be raised or lowered through a threaded hole V that is at the centre of the frame denoted by F. The triangular metallic frame F is supported on three legs of equal length A, B and C. A vertical scale that is denoted by letter P marked in millimetres or half-millimetres, is known as the main scale or pitch scale. It is also fixed parallel to the central screw, which is at one end of the frame F. This scale is kept very close to the disc rim denoted by letter D but it does not touch the disc D. This scale generally reads the vertical distance when the central leg moves through the hole V.
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Spherometer Experiment Procedure
Raise the central screw of the spherometer and then press the spherometer gently on the practical note-book to get pricks of the three legs. Then we need to mark these pricks as A, B and C.
Then measure the distance between the pricks and the points by joining the points to form a triangle ABC.
We need to note these distances which are: AB, BC, AC on a notebook and take their mean.
Then we need to find the value of one vertical pitch scale division.
Then determine the pitch and the least count of the spherometer and record it stepwise.
Raise the screw upwards sufficiently.
Place the spherometer on the convex surface so that its three legs rest on it.
Then we need to gently turn the screw downwards till the screw tip just touches the convex surface.
Now note the reading of the circular disc scale which is in line with the vertical scale pitch.
Remove the spherometer from over the convex surface and place IT over a large size glass plane slab.
Then turn the screw downwards direction and count the number of complete rotations(n1) made by the disc. One rotation becomes complete when the reference reading crosses past the pitch scale.
We need to continue till the tip of the screw just touches the plane surface of the glass slab.
Note the reading of the circular scale which is finally in line with the vertical pitch scale. Let it be denoted by letter b.
Now find the number of circular disc scale divisions in the last rotation which is incomplete.
Record the observation in tabular form.
The Calculations Part:
1. We need to find the value of h in each observation and record it in the column.
2. Then find the mean of the value of h that is recorded in the column.
The Result:
The radius of curvature of the given convex surface is cm.
The Precautions:
The screw should move freely without friction.
The screw which we are talking about should be moved in the same direction to avoid the back-lash error of the screw.
Excess rotation that should be avoided.
The Sources of Error
The screw may have friction.
The spherometer generally may have a back-lash error.
The circular disc scale divisions may not be of equal size.
What is Spherometer
A spherometer is said to be an instrument for the precise measurement of the radius of curvature of a sphere or that of a curved surface. Originally these instruments were primarily used by opticians to measure the curvature of the surface of a lens.
FAQs on How to Determine Radius of Curvature of a Spherical Surface Using a Spherometer
1. What is a spherometer and what is its primary use in a physics lab?
A spherometer is a precision instrument used to measure the radius of curvature of a spherical surface, like a lens or a curved mirror. It can also be used to measure the thickness of thin, flat objects like a glass slide. Its name is derived from its primary function of measuring spheres.
2. On what principle does a spherometer work?
The working principle of a spherometer is the same as that of a micrometer screw. It relies on the precise conversion of a known rotational movement of a screw into a very small, measurable linear movement. The vertical distance the central screw moves is measured using a main scale and a circular scale.
3. How is the least count of a spherometer calculated?
The least count (LC) of a spherometer, which is the smallest distance it can accurately measure, is calculated using the formula:
Least Count = Pitch / Number of divisions on the circular scale
Where the 'pitch' is the vertical distance moved by the central screw in one complete rotation of the circular disc.
4. What is the formula used to determine the radius of curvature (R) with a spherometer?
The formula to calculate the radius of curvature of a spherical surface using a spherometer is:
R = (l² / 6h) + (h / 2)
Where:
- l is the average distance between any two of the outer legs of the spherometer.
- h is the sagittal height, which is the height or depth of the curved surface measured by the central screw.
5. What is the importance of measuring 'h' for both convex and concave surfaces?
The measurement of 'h' (sagittal height) differs for the two types of surfaces:
- For a convex surface (like the back of a spoon), the central screw is raised from the plane level.
- For a concave surface (like the inside of a watch glass), the central screw is lowered below the plane level.
6. Why is it essential to take the mean distance 'l' between the spherometer's legs?
It is essential to measure the distance between all three pairs of legs (AB, BC, CA) and then calculate the mean value 'l'. This is because minor manufacturing imperfections can cause the legs not to form a perfect equilateral triangle. Averaging the distances minimizes this potential source of error and leads to a more accurate calculation of the radius of curvature.
7. How do you identify and correct for zero error in a spherometer?
Zero error exists if the zero mark of the circular scale does not coincide with the main scale line when the tip of the central screw and the tips of the three legs are on a perfectly flat surface (like a plane glass slab).
- If the zero mark is below the main line, the error is positive.
- If the zero mark is above the main line, the error is negative.
8. What are some key precautions to take while performing the spherometer experiment?
For accurate results, a student should observe the following precautions:
- The screw should be moved in the same direction (preferably downwards) to avoid backlash error.
- The spherometer should be placed gently on the surfaces.
- Readings should be taken without parallax error by keeping the eye directly above the scale.
- The central screw should only just touch the surface; overtightening can damage the surface and give incorrect readings.
