# How Does a Spherometer Measure Curvature?

• blackcat
In summary, the conversation is about using a spherometer, a device with three fixed legs and one adjustable leg that is used to measure the curvature of a lens. The distance between the fixed legs and the distance the adjustable leg is moved are used in a formula to calculate the radius of curvature. There is also a diagram available for reference.
blackcat
I'm trying to figure out what/how to use one without seeing/having one.

Am I right in saying the following.

It has three legs, which form the vertices of an equilateral triangle. The centre leg is placed onto a lens, and it's adjusted until they all balance/evne out. Then the distance of it has been adjusted is noted, and put into this formula (on wikipedia I found);

r = [ (a^2 + 3h^2)/6h ]

in which a = distance between feet, and h is the distance it's been adjusted.

Is there a diagrammatical representation of this? Can someone correct any mistakes?

Thanks

blackcat said:
I'm trying to figure out what/how to use one without seeing/having one.

Am I right in saying the following.

It has three legs, which form the vertices of an equilateral triangle. The centre leg is placed onto a lens, and it's adjusted until they all balance/evne out. Then the distance of it has been adjusted is noted, and put into this formula (on wikipedia I found);

r = [ (a^2 + 3h^2)/6h ]

in which a = distance between feet, and h is the distance it's been adjusted.

Is there a diagrammatical representation of this? Can someone correct any mistakes?

Thanks
There are three fixed legs separated by distance a and an adjustable leg in the center of the triangle.

http://physics.kenyon.edu/EarlyApparatus/Optics/Spherometer/Spherometer.html

The flat disk is engraved with the markings to show the d value. The vertical flat is aligned with the markings to read d.

Using a spherometer may seem daunting at first, but with a little guidance, it can be a valuable tool in measuring the curvature of lenses and other curved surfaces. The first step is to ensure that the spherometer is set up correctly. As you mentioned, it has three legs that form an equilateral triangle. The center leg should be placed on the surface you want to measure, while the other two legs should be resting on a flat surface. This will ensure stability and accuracy in your measurements.

Next, you will need to adjust the center leg until it is level with the other two legs. This can be done by turning the knob on top of the center leg, which will raise or lower it. Once all three legs are level, you can take your measurement. The distance the center leg was adjusted is important, as it will be used in the formula you mentioned (r = [(a^2 + 3h^2)/6h]). The "a" in this formula refers to the distance between the outer two legs, and the "h" refers to the distance the center leg was adjusted. This formula will give you the radius of curvature of the surface you are measuring.

To answer your question about a diagrammatical representation, there are several diagrams available online that show the setup and use of a spherometer. It may also be helpful to watch a video tutorial or have someone demonstrate the process for you in person.

I hope this explanation helps you understand how to use a spherometer. It may take some practice to get comfortable with, but with proper setup and use, it can be a valuable tool in your scientific endeavors.

## 1. How do I calibrate a spherometer?

To calibrate a spherometer, place it on a flat surface and adjust the three screws on the base until all three legs are touching the surface. Then, use a micrometer to measure the distance between the base and the top of the center screw. This measurement is known as the "pitch" and should be recorded for future use.

## 2. How do I measure the radius of a spherical object with a spherometer?

To measure the radius of a spherical object, place the object on a flat surface and place the spherometer on top of it. Adjust the screws on the base until all three legs are touching the surface of the object. Use the micrometer to measure the distance between the base and the top of the center screw. This measurement, along with the pitch measurement from calibration, can be used to calculate the radius using the formula: R = (2P + d)/6, where R is the radius, P is the pitch, and d is the distance measured with the micrometer.

## 3. How do I use a spherometer to measure the thickness of a lens?

To measure the thickness of a lens, place the lens on a flat surface and place the spherometer on top of it. Adjust the screws on the base until all three legs are touching the surface of the lens. Use the micrometer to measure the distance between the base and the top of the center screw. This measurement, along with the pitch measurement from calibration, can be used to calculate the thickness of the lens using the formula: t = (P^2 + d^2)/2P, where t is the thickness, P is the pitch, and d is the distance measured with the micrometer.

## 4. Can a spherometer be used to measure the curvature of a mirror?

Yes, a spherometer can be used to measure the curvature of a mirror. Place the spherometer on the mirror and adjust the screws on the base until all three legs are touching the surface. Use the micrometer to measure the distance between the base and the top of the center screw. This measurement, along with the pitch measurement from calibration, can be used to calculate the radius of curvature using the formula: R = (2P - d)/6, where R is the radius of curvature, P is the pitch, and d is the distance measured with the micrometer.

## 5. What factors can affect the accuracy of spherometer measurements?

The accuracy of spherometer measurements can be affected by a few factors, including the flatness of the surface being measured, the precision of the micrometer, and any imperfections or damage to the spherometer itself. It is important to calibrate the spherometer before each use and to ensure that the surface being measured is as flat as possible to achieve the most accurate results.

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