Interactive Simulation

h
Contact Made!
0 mm 10 mm
Tip: Slowly adjust until the contact indicator appears

How to Calculate

1 Set Plane Reading (R₁) when contact is made on flat surface
2 Set Sphere Reading (R₂) when contact is made on curved surface
3 Formula: R = (l²/6h) + (h/2)
4 Where: h = R₂ - R₁ (sagitta)

💡 Tip: Look for the red contact indicator before setting readings!

Instrument Readings

Magnified Scale View
Main Scale (MSR)
5.00 mm
Circular Scale (CSD)
0

Total Reading = MSR + (CSD × L.C.)

5.000 mm

Calculation

Pitch: 1 mm
Least Count (L.C.): 0.01 mm
Distance between legs (l): 4.0 cm
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Spherometer Theory

A spherometer is an instrument used to measure the radius of curvature of spherical surfaces. It consists of a central screw and three outer legs that form an equilateral triangle.

Principle

The spherometer works on the principle of measuring the sagitta (h) - the vertical distance between the plane of the three outer legs and the point where the central screw touches the surface.

Formula

The radius of curvature (R) is calculated using the formula:

R = (l² / 6h) + (h / 2)

Where:

  • R = Radius of curvature
  • l = Distance between any two legs of the spherometer
  • h = Sagitta (difference in readings between plane and spherical surfaces)

Procedure

  1. Find the Zero Reading: Place the spherometer on a plane surface and adjust the central screw until it just touches the surface. Record this reading as R₁.
  2. Place on Spherical Surface: Place the spherometer on the spherical surface whose radius of curvature is to be measured.
  3. Take Reading on Sphere: Adjust the central screw until it just touches the spherical surface. Record this reading as R₂.
  4. Calculate Sagitta: Calculate h = R₂ - R₁
  5. Calculate Radius: Use the formula to calculate the radius of curvature R.

Least Count

The least count of a spherometer is given by:

Least Count = Pitch / Number of divisions on circular scale

For a typical spherometer with pitch = 1 mm and 100 divisions on the circular scale, the least count is 0.01 mm.