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# Determine Radius of Curvature of a Given Spherical Surface by a Spherometer      LIVE
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## An Introduction

Class 11 students are expected to know the exact spherometer experiment procedure. You will need to determine the radius of curvature of given spherical surfaces using this device. However, before proceeding to learn about the process of doing the same, one should understand spherometers in detail.

### What is a Spherometer?

A spherometer is one of the vital scientific devices that measure the radius of curvature for any spherical surface precisely. Initially, opticians used these devices to create and determine powered lenses.

We come across various instruments that are used in a lab for the measurements of different things but when we have to measure the radius of curvature of either a sphere or a curved surface with its precise measurements, then we use an instrument called a spherometer. Now if you look back at the history of the spiral meter we see that it was invented by Robert-Aglaé Cauchoix, his profession was that of an optician in the year 1810. Robert mainly manufactured the spherometer for the use of opticians in grinding lenses. Other than using it for grinding lenses or in the physics lab, sphere meters are used by astronomers for grinding lenses and curved mirrors. Accordingly, spherometers can have various other uses as well.

Now before we go ahead with the understanding and definition of the spherometer we will see the working principle of the device. The working principle of a spherometer is based on a micrometer screw which is used for measuring a small thickness of flat material such as gas or can be used for measuring the radius of curvature of a spherical surface.

Normally a spherometer can be described as a device consisting of a base of a  circle of three of the leg, central leg and a reading device. The Circle of three or three legs is also known as the radius of the base Circle and the land along with it is known as the radius of the base circle, the outer legs which are given can be adjusted accordingly depending on the inner holes, this procedure is mainly done to accommodate smaller surfaces. The central leg of the spherometer can be moved in an upward and downward direction accordingly, this can be called a flexible method of drawing lines or using it with any other measurements. For taking the measurements any device on the reading device should be moved accordingly.

### How to use a Spherometer?

A spherometer is a very common device in labs, opticians, and other physics-related settings but the main thing that is necessary is to know and understand how to use a spherometer. There is a certain set of procedures that are included while using a speedometer:

• After holding the instrument, it is first placed on the perfect plane surface in a manner that the middle foot is screwed down slowly till it touches the surface below. After the middle foot touches the surface, the instrument turns around on the middle foot as the center, now the center has a point from which we can equally draw shapes accordingly or measure.

• After the surface is made the spherometer is then carefully removed from the surface to take the readings from the micrometer screw. The instrument should show the reading 0-0 in normal cases, this reading comes when the instrument is working fine, any other reading might lead to errors. If there is any sort of slight error in the instrument it could be either a negative or positive error.

• Now, when we measure the instruments reading, we take the instrument of the plane and let the middle foot back.

• When we are measuring we come across a reading below the zero line so if we see that reading it should be added to the zero error. If the reading above the zero lines is indicated then the reading should be subtracted from the zero error in order to make it balanced.

• To measure the length between the two legs, the instrument should be placed on the plane surface or a playing card while using a meter scale so that equal length is measured

To measure the radius of curvature using a spherometer, one must know its various parts. The device has a screw with a moving nut in the middle of a frame with three small legs to support it upright. The table legs, along with the screw, have tapered points to help them rest on a specific surface.

Additionally, a spherometer’s least count can differ from one device to another and each time that we may use it to determine the radius of curvature, we still need to calculate this acquired count again.

### Define Spherometer Least Count

The smallest value that a spherometer can measure is known as its least count. The formula for determining the least count is as follows –

Least count = Pitch/Number of divisions on its head scale

Typically, the least count is always 0.01 mm.

### Experiment to Find Radius of Curvature using Spherometer

1. Aim

To find the radius of curvature using spherometer of a spherical surface

1. Apparatus Necessary

Plane mirror, spherometer and convex surface

1. Table Format for Noting Experiment Data

 Serial No. Circular Scale Reading No. of complete rotations (n1) No of scale divisions in incomplete rotationsX = (a-b) Total readingh = n1 x p + x (L.C) in mm On convex surfaces Initial (a) On plane glass sheet Final (b) 1. h1 = 2. h2 = 3. h3 =

### Complete Procedure for the Experiment

• Step 1: Raise the central screw of this device and use a paper to track the position of a spherometer’s three legs. Join these three points on the paper and mark them A,B and C.

• Step 2: Measure the minute distance between the three points. Note the three distances (AB, BC and AC) on a sheet of paper.

• Step 3: Determine the value of one pitch (or one vertical division).

• Step 4: Record the least count of your spherometer.

• Step 5: Raise the screw upwards to prepare for the measurement.

• Step 6: Place this spherometer on the spherical surface in such a manner that all three legs are resting on the object.

• Step 7: Start turning the screw so that it barely touches this convex surface.

• Step 8: Take the reading of both the vertical scale and the disc scale in such a position. This will act as your reference point.

• Step 9: Now place this spherometer on a plane glass slab.

• Step 10: Move the screw downwards and count the number of complete rotations for the disc (n1).

• Step 11: Continue moving until the screw tip touches the glass slab.

• Step 12: Note the reading (b) on this circular scale in relation to its vertical scale.

• Step 13: Note the circular divisions for its last incomplete rotation.

• Step 14: Complete steps 6 to 13, thrice. Note readings each time in the tabular format mentioned above.

### Observations

• Mean Value of AB, BC and AC

Mean value or l = $\frac {AB + BC + AC}{3}$

• Mean Value of h

h = $\frac {h_1 + h_2 + h_3}{3}$mm (Convert into cm)

Radius R = $\frac {I^2}{6h}$ + $\frac {h}{2}$ cm

Last updated date: 21st Sep 2023
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## FAQs on Determine Radius of Curvature of a Given Spherical Surface by a Spherometer

1. What is the Value of R for a Plane Surface?

Radius of curvature R only exists for spherical surfaces. Therefore, R for a plane surface will always be zero.

2. What is this Formula to Calculate Radius of Curvature Using a Spherometer?

Radius R =  $\frac {1^2}{6h}$   + $\frac {h}{2}$ cm  is the formula which is used to calculate the radius of curvature of a spherometer.

3. What is the Formula to Measure the Least Count of Spherometers?

You can determine the least count of a spherometer by dividing the pitch of the device by the number of divisions on a circular scale.

4. What is the use of a spherometer?

A spherometer is an instrument used for the precise measurement of the radius of curvature of a sphere or a curved surface.

5. What is the least count of a spherometer?

The least count can be defined as the distance moved or covered by the crew of the spherometer when turned through 1 division on the circular loop. The least count can be calculated using the formula, The formula for the radius of curvature of a spherical surface. The least count of the spherometer can be measured by dividing the pitch of the spherometer screw by the number of divisions on the circular scale.