Experiment 13 Thin Lens

Experiment 13 Thin  Lens

Topic: Geometrical Optics Title: Thin lens

Purpose: To measure the refractive index of a lens 

Theory:

From the lens maker's formula, the focal length f of a thin lens is given by 

where n is the refractive index of the lens, and and are the radii of curvature of the surfaces of the lens.

The focal length of the lens can be determined by non-parallax method. The radii of curvature of the surfaces of the lens can be determined using a spherometer. The refractive index n can be found from the equation above.

The Figure 22 below shows a method to determine the radius of curvature using a spherometer with r the radius of curvature and x the distance between the centre leg and one of the fixed legs.

From Figure 22

The four legs of spherometer can be represented as in Figure 23 where A, B and C are the fixed leg and O is the centre leg.

From Figure 23

The radius of curvature is obtained using the equation below. 

Apparatus:

(i)    A spherometer

(ii) A glass block

(iii) A convex lens

(iv) An optical pin

(v) A plane mirror

(vi) A retort stand with clamp

(vii) A half-metre rule

Procedure:

Part 1: To measure the radius of curvature by using a spherometer

(a) Place the spherometer on a plane glass block and lower the centre leg until it just touches the block.

(b) Measure and record this zero reading as .

(c) Place the spherometer on the curve surface of the lens. Adjust the centre leg until all the four legs touch the curved surface.

(d) Measure and record the reading of spherometer as . The difference in readings  gives the height of the centre leg above the other three.

(e) Press the three fixed legs on a pad of papers to make indentations.

(f) Draw a triangle as in Figure 23.

(g)    Measure and record the distance between the fixed legs d.

(h)    Determine the radius of curvature .

(i)    Repeat steps (c) and (d) to determine the radius of curvature . 

Part II: To determine the focal length of a convex lens

  (a)    Set-up the apparatus as in Figure 24.

(b)    Clamp an optical pin on the retort stand so that it is vertically above the centre of the convex lens.

(c)    Using non-parallax method, adjust the position of the optical pin until the image coincides with it.

(d)    Measure and record the height s of the pin above the plane mirror. The focal length of the lens f equals to s.

(e)    Determine the refractive index of the len.