Question

If $h$ be the elevation or depression of a spherical surface from the plane glass plate and $c$ be the mean difference between two consecutive points corresponding to the impressions made by the three legs of a spherometer, then the radius of the curvature is:
A. $\dfrac{{{c^2}}}{{6h}} - \dfrac{h}{2}$
B. $\dfrac{{{c^2}}}{{6h}} + \dfrac{{{h^2}}}{2}$
C. $\dfrac{{{c^2}}}{{6h}} + \dfrac{h}{2}$
D. $\dfrac{{{c^2}}}{{6h}} + \dfrac{2}{h}$

Answer 1

Hint:- In this question, we have to find the Radius of curvature. And according to the formulae of Radius of curvature, we have already given the elevation and the Average distance of the three legs of the spherometer.

Complete step by step solution:
Given that-
From plane glass plate to the spherical surface, the elevation or depression is supposed to be $h$ . And, the mean difference between both the consecutive points corresponding to the impressions made by the three legs of a spherometer is supposed to be $c$ .
The spherometer used for measuring the radius of curvature of spherical surfaces, and we have to also find here the radius of curvature, is explicitly based on a geometric relation unique to circles and spheres.
So, in this device or instrument, if $h$ is the elevation of a spherical surface and $c$ is the mean difference between two consecutive points corresponding to the impressions made by the three legs.
Now, we have the formulae of Radius of Curvature of the spherical surface is as follows:
$R = \dfrac{{{d^2}}}{{6h}} + \dfrac{h}{2}$
In the above formulae, $d$ is the Average distance of the three legs of the spherometer which is given as $c$ .
$R = \dfrac{{{c^2}}}{{6h}} + \dfrac{h}{2}$

Hence, the correct option is option(C) $\dfrac{{{c^2}}}{{6h}} + \dfrac{h}{2}$.

Note:- A spherometer consists of a metallic tripod framework. It was 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.