Spherometerdiagram

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The vertical distance moved by the screw S in one complete rotation of the circular Scale/Disc D is called the pitch (p) of the spherometer. To find the pitch, give full rotation to the screw (say 4 times) and note the distance (d) advanced over the pitch scale.

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Spherometerleast count

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From the figure 3.4, the circle is passing through A and C.  O is the centre of the circle. OE =R, radius of the circle. F is the tip of the screw at the same plane with A, B and C. CF = h, AF = a ∠EAC = 900.

Spherometeris used to measure

The Least count (LC) is the distance moved by the spherometer screw, when the screw is turned through 1 division on the circular. We are using a spherometer which has 100 divisions (N) on the disc. The least count can be calculated using the formula,

Spherometermeasures

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Now, let l be the distance between any two legs of the spherometer or the side of the equilateral triangle ABC (Fig. 3.4), then from geometry we have, a = l/√3. Thus the radius of curvature of the spherical surface can be given by,

Spherometerphysics

A spherometer is a measuring instrument used to measure the radius of curvature of a spherical surface and a very small thickness.

A Foucault knife edge test is a method used to measure the curvature of a mirror or lens. It is named after the French physicist Léon Foucault, who developed the technique in the 19th century.

From the figure 3.3, O is the centre of the circle. OE = OA = R, radius of the circle. F is the tip of the screw at the same plane with A, B and C. EF = h, AF = a and ∠AFO =

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Now, let l be the distance between any two legs of the spherometer as shown in figure 3.6, then from geometry we have, a = . Thus the radius of curvature of the spherical surface can be given by,

Digitalspherometer

Field of View = Field Number (FN) ÷ Objective Magnification · Field of View = 20mm / 10 = 2.0 mm.

The basic setup for a Foucault knife edge test consists of and illuminated pinhole size source, a knife edge, and the mirror or lens being tested. The pinhole source is placed at one center of curvature of a mirror (or say twice the focal distance of a lens), and the knife edge is placed near the image of the pinhole.

Spherometerformula

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The knife edge is translated across the optical axis and the image of the light spot on a screen placed behind the lens or mirror is observed. As the knife edge is moved, the position of the light spot on the screen will change in a way that is related to the curvature of the lens or mirror. By measuring the position of the light spot on the screen as the knife edge is moved, it is possible to determine the curvature of the lens or mirror.

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Spherometerexperiment

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Figure 3.1 is a schematic diagram of a single disk spherometer. It consists of a central leg OS, which can be raised or lowered through a threaded hole V (nut) at the centre of the frame F. The metallic triangular frame F supported on three legs of equal length A, B and C. The lower tips of the legs form three corners of an equilateral triangle ABC and lie on the periphery of a base circle of known radius, r. The lower tip of the central screw, when lowered to the plane (formed by the tips of legs A, B and C) touches the centre of triangle ABC. A circular scale (disc) D is attached to the screw.  The circular scale may have 50 or 100 divisions engraved on it. A vertical scale P marked in millimetres or half-millimetres, called main scale or pitch scale P is also fixed parallel to the central screw, at one end of the frame F. This scale is kept very close to the rim of disc D but it does not touch the disc D. This scale reads the vertical distance when the central leg moves through the hole V.