Spherometer

SPHEROMETER

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By Aditya Abeysinghe

SEE THE VIDEO FORMAT OF THIS PRESENTATION AT:

https://www.youtube.com/watch?v=DRu-6D7mlBU

See more of my videos at :https://www.youtube.com/channel/UCVFSs7LUN4DSr0a4kkGt4Ag

Spherometers are small precision instruments for measuring the radius of curvature of spherical surfaces. They can also be used to measure the thickness of a thin plate.

INTRODUCTION

PARTS OF A SPHEROMETER

Reading for convex surfaces

Zero of vertical scale

Reading for concave surfaces

Circular scale

Legs

Central leg or middle screw

Base circle

Screw head

Pitch- Pitch is the distance moved by the middle screw per revolution

Pitch may vary for different spherometers

Least count = Pitch / No.of divisions on the circular scale

E.g.: The least count for a spherometer of 100 equal divisions and of pitch 0.5 mm is,

Least count = 0.5mm/100 =0.005mm

SPECIAL DEFINITIONS ON SPHEROMETER MEASUREMENTS

Radius of curvature of a curved mirror is the radius of the sphere that was used to make it.

RADIUS OF CURVATURE

R

C

R – Radius of curvatureC- Center of the sphere

To measure the radius of curvature, we place the spherometer on the mirror as follows:

BUILDING AN EXPRESSION FOR THE MEASUREMENTS

When you keep the spherometer on the mirror it will be as follows:

h

RR

R - h

x

From Pythagoras theorem,R2 = x2+ (R-h)2

R2 = x2+ R2 + h2 - 2RhR = (x2+ h2 ) / 2h

*However, practically, it’s hard to measure x. So, what we do is that we express the above relationship using the distance between the legs.

When you keep the spherometer on any surface, the legs will form an equilateral traingle.

See figure below.

If we take the distance between legs to be ‘a’

a

a/2 a/2

30°

x

Finally you can simplify the shape to -

x

a/2

30°

Therefore, x cos 30° = a/2Thus, x = a / √3

Now, R = (x2+ h2 ) / 2hBy substituting for x,R = ((a / √3 )2 + h2 ) / 2hTherefore, R = (a2/6h) + (h/2)

Now that we have built a relationship for R, we can measure R of both concave and convex surfaces

RADIUS OF CURVATURES

h

RR

R - h

x

For convex surfaces For concave surfaces

x h

RR

R - h

1. Place the spherometer on a plane mirror and adjust the center leg or the screw so that the screw and the three legs are on the same plane.(It’s always better to check whether the object and the image are in contact on keeping on the plane mirror)

MEASURING USING A SPHEROMETER

MatchingNot matching

2. Then read the measurement, as placed in step 1, using the vertical and circular scales. Take this to be x.

3. Then keeping the 3 legs in place, move the screw upwards so that the object to be measured now is below the screw.

4. Then adjust the screw so that the screw is just touching the surface of the object to be measured.

5. Then take the reading at that instance using the vertical and circular scales. Take this to be y.

6. Thus, the height of the object is the difference between these heights.

Therefore, h = y – x.

7. Now to measure the radius of curvature, if the object used is a spherical object, first measure the distance between the legs using a vernier caliper

(Using a vernier caliper is recommended as the object can be tightly placed between its outer jaws)

8. Finally, use the formula derived for R to find the radius of curvature.