What is Spherometer?
A spherometer is defined as
An instrument that is used for precise measurements of the radius of curvature of either sphere or a curved surface.
The first spherometer was invented by Robert-Aglae Cauchoix who was a French optician in 1810. These were primarily manufactured for the use of opticians in grinding lenses. Astronomers also used this instrument in grinding lenses and curved mirrors.
Spherometer Diagram
Spherometer Working Principle
The working principle of a spherometer is based on the micrometer screw. It is used for measuring with a small thickness of flat materials such as glass or for measuring the radius of curvature of a spherical surface.
Parts of Spherometer
A spherometer generally consists of a base circle of three outer legs, a central leg and a reading device.
- A spherometer consists of a base circle of three outer legs, which is also known as the radius of the base circle, a ring with a known radius of the base circle.
- The outer legs of the spherometer can be adjusted according to the inner holes. This is done to accommodate smaller surfaces.
- The central leg can be moved in an upward and downward direction.
- For taking the measurements, the reading device on the central leg should be moved.
Principles of Operation
If R is the radius of spherical material, then the mean length between two outer legs can be determined by using the formula:
\(\begin{array}{l}R=(\frac{h}{2})+(\frac{a^{2}}{6h})\end{array} \) |
Where h is the sagittal measure.
The spherical radius R can be determined by a different spherometer without legs and with circle cup and dial gauge, D is given by the formula:
\(\begin{array}{l}R=(\frac{h}{2})+(\frac{D^{2}}{8h})\end{array} \) |
Least Count of Spherometer
Number of divisions on the circular scale = 100
Distance moved by the screw in 10 complete rotations = 10 mm
Pitch = Distance moved/number of complete rotations
Least count = Pitch/number of divisions on the head scale = 1/100 = 0.01 mm
How to use a Spherometer?
The following is the procedure to use spherometer:
- The instrument is first placed on the perfect plane surface such that the middle foot is screwed down slowly till it touches the surface. When the middle foot touches the surface, the instrument turns rounds on the middle foot as the centre.
- The spherometer is then carefully removed from the surface to take the reading from the micrometre screw. If the instrument is working fine, then the reading should be 0-0. However, there is always a slight error in the instrument which could be either a positive or negative error.
- Take the instrument off the plane and draw the middle foot back.
- Let’s consider that we are measuring the radius of the sphere from the convex side.
- Now read the scale and screw-head. If the reading is 2.0 and 0.155, then the total reading is 2.155.
- If the reading is below the zero lines, then the reading should be added to the zero error. If the reading is above the zero lines then the reading should be subtracted from the zero error.
- To measure the length between the two legs, the instrument should be placed on the plain card and using a meter scale the length should be measured.
- Now, calculate the radius of curvature using the following equation:
\(\begin{array}{l}r=(\frac{l^{2}}{6a})+(\frac{a}{2})\end{array} \) |
Read more:
| To Determine Radius Of Curvature Of A Given Spherical Surface |
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Frequently Asked Questions – FAQs
Why does a spherometer have three legs?
A spherometer has three legs so that it forms an equilateral triangle. The three legs of the spherometer are used for measuring both positively and negatively curved surfaces.
How to find the zero error in a spherometer?
A spherometer does not have a zero error because the result obtained is by taking the difference between the final and initial reading.
Why is a spherometer so called?
A spherometer is so-called because it is used for measuring the radii of curvature of spherical surfaces.
What is the pitch of spherometer?
The pitch is defined as the distance covered by the circular disc in one complete rotation along the main scale. Therefore, the pitch of a spherometer is given as 1 mm = 0.1 cm.
What is zero error in a spherometer?
The zero error in a spherometer is equal to the reading on the plane glass sheet.
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