# How to determine the radius of curvature of a given spherical surface (Concave mirror or Convex mirror) with the help of a Spherometer

Experiment : To determine the radius of curvature of a given spherical surface (Concave mirror or Convex mirror) with the help of a Spherometer .

Apparatus : Spherometer , a spherical surface (concave mirror or convex mirror ) , plane glass slab , a Vernier calliper , wooden blocks

Measurement of Radius of curvature of a spherical surface

The radius of curvature R of a concave or convex surface is given by relation .

$\displaystyle R = \frac{l^2}{6h} + \frac{h}{2}$

Where h represents the height of the central screw below or above the plane of legs of spherometer .

h = m × Pitch + X × Least count

Where m represents number of complete rotations and X represents number of additional circular scale divisions moved . An equilateral triangle of side is formed by pressing spherometer on it . Get means of three sides of equilateral triangle .

How to Perform : (For Convex Mirror)

(i) Determine the least count of Spherometer

(ii) Raise the screw

(iii) Keep it on Notebook and press . Mark the position of three points accurately

(iv) Measure the length of every side of edge of triangle formed by joining these points very accurately with the help of projecting jaw of vernier calliper and calculate mean .

(v) Raise the middle leg through four or five rotations of circular scale . Keep the convex mirror strongly on a horizontal surface . Keep the spherometer on the polished surface of convex mirror , turn the screw so that the middle sharp leg when moving downwards just touches the surface of the mirror .

(vi) Note down the circular scale reading against the edge of the vertical scale .

(vii) Keep the spherometer on a plane glass slab . Turn the screw by the time tip of middle leg just touches the plane surface .

(viii) Count the number of complete rotations and the number of the circular divisions moved .

(ix) Repeat the above measurements (raise screw through distance bigger than h) three times .

For Concave Mirror : Fix the mirror strongly in place between the blocks of wood . Take the circular scale reading by keeping the spherometer first on the plane glass slab and then on the polished concave surface .

Obervation:

(i) Pitch of the screw = …mm

(ii) Total number of divisions on circular scale = N

(iii) Least count of the spherometer = …mm

(iv) Mean Distance between the legs l = ….cm

$\displaystyle l = \frac{AB + BC + CA}{3}$

Calculations :

Radius of curvature for convex mirror R = ….cm , Formula $\large R = \frac{l^2}{6h} + \frac{h}{2}$

Outcome : Radius of curvature of convex mirror R = ….cm

Precautions:

(i) Escape backlash error

(ii) Escape excess rotation

(iii) The screw must be frictionless

Sources of Error :

(i) Friction in screw

(ii) Backlash error