Spherometer

This presentation explains about the usage of a spherometer to take measurements. First part includes the definition and the description of its parts while the second part explains as to how different measurements can be taken.

1. Spherometer See more at: Facebook –https://www.facebook.com/AdityaAbeysinghePresentations Slideshare - slideshare.net/adityaabeysinghe Wordpress - adityaabeysinghepresentations.wordpress.com/abeysinghe-foundation/ ‎ By Aditya Abeysinghe

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3. 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

4. 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

5. 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

6. 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 curvature C- Center of the sphere To measure the radius of curvature, we place the spherometer on the mirror as follows:

7. Building an expression for the measurements When you keep the spherometer on the mirror it will be as follows: h R R R - h x From Pythagoras theorem, R 2 = x 2 + (R-h) 2 R 2 = x 2 + R 2 + h 2 - 2Rh R = (x 2 + h 2 ) / 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.

8. 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/2 Thus, x = a / √3 Now, R = (x 2 + h 2 ) / 2h By substituting for x, R = (( a / √ 3 ) 2 + h 2 ) / 2h Therefore, R = (a 2 /6h) + (h/2)

9. Now that we have built a relationship for R, we can measure R of both concave and convex surfaces Radius of curvatures h R R R - h x For convex surfaces For concave surfaces x h R R R - h

10. 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 Matching Not matching

11. 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.

12. 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.