Determine Radius of Curvature of a Given Spherical Surface by a Spherometer

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 measures the radius of curvature for any spherical surface precisely. Initially, opticians used these devices to create and determine powered lenses.

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To measure the radius of curvature using 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, least count of spherometers differs from one such device to another. Therefore, each time that you use it to determine radius of curvature, you need to calculate this count.

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

Now that you know some of this measuring device’s basics, let us learn more about this experiment in general.

  1. Aim

To find 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 rotations

X = (a-b)

Total reading

h = 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 = AB + BC + AC/3

  • Mean Value of h

h = h1 + h2 + h3/3 mm (Convert into cm)

Calculating Radius of Curvature of Convex Lens using Spherometer Readings

Radius R = l2/6h + h/2 cm

Vedantu’s interactive classes can help you understand more about spherometer readings, radius of curvature and more. Experienced teachers are at your disposal whenever you need your doubts cleared. Now you can also download our Vedantu app for better access to these study materials and online interactive sessions.

FAQ (Frequently Asked Questions)

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

Ans. 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?

Ans. R = l2/6h + h/2 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?

Ans. 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.