# Learn All About Spherometer From This Teacher.

A spherometer consists of a metallic tripod framework. It supported on three fixed legs of equal lengths. A screw passes through the center of the tripod frame. A circular disc with 100 equal parts is attached to the top of the screw.

This device was built using the screwdriver principle. This is mainly used to measure the radius of curved surfaces. But this can be used to find the thickness of any objects such as plates or glass slides. The thickness can be accurately measured in two decimal places because the smallest measure is 0.01mm. Therefore the readings should be shown in two decimal places in millimeters such as 2.23mm. This matter is very important to us. After examining the video with practical exams, the subject matter can be better understood. The following diagram shows a Spherometer.

Parts of the Spherometer :

A, B, C, –  Legs
D – Central leg or middle screw
E – Circular Scale
G – linear scale or pitch scale ( Reading for convex and concave surfaces )

First, we want to find the pitch of the Spherometer.

The number of complete rotation made by the circular disc = n
The distance moved by the screw on the pitch scale = d
Pitch(The distance moved by the middle screw per revolution) = p
pitch p = (d/n) mm

Divisions in the circular scale on the circumference of the disc = N
Least Count = (Pitch)/(Divisions in the circular scale)
Least Count = (p/N) mm = (1/100) mm or (0.5/50) mm = 0.01 mm

There are two types of Spherometer. Which contain

1. Pitch = 0.5mm and The number of parts on the Circular Scale = 50
2. Pitch = 1mm and The number of parts on the Circular Scale = 100

## zero error in spherometer

Spherometer may have a zero error. The reading of Spherometer when 3 legs (A, B, C) and middle screw (D) are on the same plane. We can get this position by using a plane glass. First, it’s 3 legs (A, B, C) is placed on a plane glass as shown in the fig. Then Screw head is rotated clockwise until the middle screw contacts the plane glass. After that, we can read the zero error.

There are three ways to find the position that A, B, C, D points are on the same plane.

1. While we rotate the screw head,  On one occasion clockwise it’s 3 legs try to rotate clockwise by itself. Just it tries to rotate we want to stop rotating the screw head. You want to understand that A, B, C and D  points are placed on the same plane at this moment.
2. First, it’s 3 legs (A, B, C) is placed on a plane glass as shown in the fig. Next, The circular disc is fingerprinted and rotated slowly clockwise. On one occasion, fingers feel tight in motion. That is moment A, B, C and D points are the same plane.
3. First, it’s 3 legs (A, B, C) is placed on a plane glass. We can see the middle screw(D) on the glass plate. While we rotate the screw head clockwise the image of it comes slowly to touch point of middle screw. Just we see the point of the middle screw and point of its image in the glass plate are both together we stop the rotating the plate.

Z.E. in spherometer = reading on the plane glass.

## Equation for the radius of curved surface  When the point 4 is touched on a global surface as shown in the fig above, the shortest distance from the ABC plane to the screw point D is h. AB=BC=CA=a= distance between two legs. The radius of the curved surface is R.

BO=23 acos300 ​​ because the O is the center of the Equilateral triangle ABC

BO=23 a 32=3a3=a3

(BO')2=(BO)2+(OO')2

R2=(a3)2+(R-h)2=(a3)2+R2-2Rh+h2

2Rh=(a3)2+h2=a23+h2

R=a26h+h2​​

### Apparatus that we need to do this experiment :

1. Spherometer
2. A piece of plane glass
3. A Spherical glass.

### How to do this experiment

First, you find the pitch and least cont of the spherometer. Now, place the spherometer on the glass plate and rotate the screw head until middle screw point touches the glass plate. To find the moment of touching you can use one of above 3 methods. Just touch the glass plane we read the readings on the circular and linear scale. Now, rotate the screw head clockwise a specific number of rounds.

Place the spherometer on the global surface and rotate the screw head carefully until middle screw point touches the global surface. Just after it touched the surface we should read the readings. By reducing each other we can get a value for h.

Note – Sometimes Screw rotates loosely in the arm. Therefor circular scale is not fixed motion.  At that time we want to use another way.

Easy way – Place the spherometer on the glass plate and rotate the screw head clockwise until middle screw point touches the glass plane. From this position, we rotate the screw head anti-clockwise a specific number of rounds. Next count the parts that circular scale moved from the position of A, B, C, and D were on the same flat. We assume that is 200  as an example. Next, Place the spherometer on the global surface and rotate the screw head carefully until middle screw point touches the global surface. Again, Just after it touched we count the parts that circular scale moved clockwise from that position. We assume that is 157. Now find the parts that moved for by reducing each other.

parts have moved for h = 200 – 157
value for the h =  (200 – 157)*(Least count) = (200 – 150)*0.01 mm
h =  (57)*(0.01 mm) = 0.57 mm

Now we can find a value for the radius of the global surface by using the above equation for R.

## Following are the few Examples of zero error

### No zero error condition The following fig shows you this case. When 3 legs (A, B, C) and middle screw (D) are touched the same glass plane the zero line of circular scale comes on the zero line of the linear scale.

### Zero Error condition When 3 legs (A, B, C) and middle screw (D) are touched the same glass plane the zero line of circular scale has rotated anti-clockwise from the linear scale. Its Mean the edge of the plate is above the zero line of the linear scale. See the fig.

Here zero error is 5*(0.01 mm) = 0.05mm
In this case, Zero error should be positive or negative. It depends on the Convection surface or concave surface. It depends on the surface be convex or concave. In this case,

The edge of the plate is below the zero line of the linear scale. See the fig.

Here zero error is also 5*(0.01 mm) = 0.05mm
or
(50-45)*(0.01 mm) = 0.05mm