What is the Radius of the Curvature of the Spherical Surface? 

Spherical surfaces are the part of the sphere which is used to form the image as per the requirement of an object using the principle of reflection of light. There are two types of spherical surfaces: convex and concave.

The linear distance between the pole and centre of curvature is called the radius of curvature. The centre of the spherical surface is called the pole, whereas the centre of the sphere (from which the spherical surface is cut ) is called the centre of curvature. When the radius of curvature becomes infinite, the spherical mirror behaves as a plane mirror. The radius of curvature lies on the principal axis of the spherical surface.

Diagram of Spherometer

Given below is the labeled diagram of a Spherometer.

How to read Spherometer?

The following is the procedure for using a spherometer:

• First, place the instrument on the perfect plane surface, so the central leg is screwed down slowly until it touches the surface. When the central leg touches the surface, the instrument rounds on the central leg as the centre.
• Remove the spherometer from the surface to take the reading from the micrometre screw. If the instrument works fine, the reading should be 0-0. However, there is always a slight error in the instrument, which could be either a positive or negative error.
• Take the instrument off the plane and draw the central leg back.
• Let’s consider measuring the sphere’s radius from the convex side.
• Now read the scale and screw-head. If the reading is 2.0 and 0.155, then the total reading is 2.155.
• If the reading is below the zero lines, then the reading should be added to the zero error. If the reading is above the zero lines, then the reading should be subtracted from the zero error.
• To measure the length between the two legs, place the instrument on the plain card and measure the length using a meter scale.
• The radius of curvature can be calculated using the following equation:

What is the Least Count of Spherometer?

The least count (L.C) can be calculated using the relation,

Pitch of a Spherometer: The pitch is defined as the distance covered by the circular disc in one complete rotation along the main scale. Therefore, the pitch of a spherometer is given as 1 mm = 0.1 cm.

Number of circular divisions = 100

Therefore,

What is Zero Error in Spherometer?

A zero error is an error in your readings determined when the true value of what you’re measuring is zero, but the instrument reads a non-zero value. 

A spherometer does not have a zero error because the result obtained is by taking the difference between the final and initial reading.

Applications of Spherometer

The primary application of a spherometer is to measure the radii of curvature of spherical surfaces such as optical lenses, spherical mirrors, and balls. These small, high-precision optical test instruments are also used to measure the thickness of microscope slides or the depth of slide depressions.

Solved Examples for Spherometer

Ex-1. A student measures the height h of a convex mirror using a spherometer. The legs of the spherometer are 4 cm apart, and there are ten divisions per cm on its linear scale, and the circular scale has 50 divisions. The student takes two as linear scale division and 40 as circular scale division. What is the radius of curvature of the convex mirror?   

Sol: 

Ex-2. The radius of curvature of a concave mirror, measured by a spherometer, is given by

The values of I and h are 4.0 cm and 0.065 cm, respectively, where ‘I’ is measured by a meter scale and h by a spherometer. Find the relative error in the measurement of R.

Sol: 

Spherometer Experiment

Experiment Title – Use of Spherometer to Find Radius of Curvature 

Experiment Description – A spherometer is a precision instrument that measures very small lengths. Let’s determine the radius of curvature of a given spherical surface using a spherometer.

Aim of Experiment – To determine the radius of curvature of a given spherical surface by a spherometer.

Material Required – A spherometer, a convex glass surface, a plane glass plate, a pencil, a measuring scale, a paper sheet and a small piece of paper.

Procedure – 

1. Observe the given spherometer and note the value of one division of its pitch scale.
2. Observe the circular scale and note the number of divisions on it.
3. Determine the least count (L.C.) and pitch of the spherometer. Place the given flat glass plate on a horizontal plane and the spherometer on it so that its three legs rest on the plate.
4. Take a sheet of paper, place the spherometer on it, and press it gently to take the impressions of the tips of the three legs. Make an equilateral triangle ABC by joining the three impressions and measuring all the sides of the ΔABC. Determine the mean distance between two spherometer legs, l.

Take great care in measuring the length l as the term l² is used to determine curvature R of the given spherical surface.

5. Place the given spherical surface on the plane glass plate and then place the spherometer on it by raising the central screw sufficiently upwards so that the three legs of the spherometer rest on the spherical surface, as shown in the figure below. 

6. Rotate the central screw till its lower tip gently touches the spherical surface. Observe the image of the screw formed due to the reflection from the surface below to make sure that the screw touches the surface.
7. Observe the reading of the pitch scale and the divisions of the circular scale that is in line with the pitch scale to take the spherometer reading h₁. Record the observations in the observation table. 
8. Remove the spherical surface and place the spherometer on the plane glass plate. Turn the central screw till its lower tip gently touches the glass plate. Again, take the spherometer reading h₂ and record it in the observation table. The difference between h₁ and h₂ equals the value of sagitta (h).
9. Repeat steps (5) to (8) three more times by rotating the spherical surface without disturbing its centre. Find the mean value of h.

Precautions – 

1. The screw of the spherometer may have friction. 
2. The spherometer may have a backlash error. 

FAQs on Spherometer