# Optics and Convex Lens

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Physics Project Aim: To find refractive indices of water and turpentine oil using a plane mirror, a equiconvex lens (made from a glass of known refractive index) and an adjustable object needle. Apparatus: A convex lens, an optical needle, a plane mirror, a clamp stand, a spherometer, a plumb line, metre scale, water and turpentine oil. Theory: Let’s add small amount of water on a flat, plane surface and place a convex lens over it. This forms a plano-concave lens of water between the lower surface of convex lens and plane mirror.

Let f1 and f2 are the focal lengths of water lens and convex lens respectively, then focal length of the combination is: The focal length of the plano-concave lens is, …(i) From Lens Maker’s formula, =(R1 = R and R2 = ())() for water lens. 1? The refractive index of water is, …() (where ‘R’ is the radius of curvature of the concave surfaces of the plano-concave lens). The Radius of curvature of the lens, is …(i) Procedure: I. For finding the focal length of convex lens: (i) () Measure the rough focal length of the convex lens.

Place the plane mirror with the convex lens placed on it above the horizontal base of a clamp stand horizontally as its tip lies vertically above the optical centre of the lens. Adjust the needle at a height a little more than the rough focal length of the convex lens. (i) Try to remove the parallax between the tip of the object needle and its image tip. (iv) Note the distance of the tip of the needle from the centre of the upper surface of the lens. Let it be x1. (Use plumb line). (v) Remove the convex lens and measure the distance of the tip of the needle from the plane mirror.

Let it be x2. (Use plumb line). 2? (vi) Repeat and record all the observations. . For finding the focal length of the plano-concave lens: Pour few drops of water over the plane mirror and place the convex lens over it. Repeat steps () to (iv) as done above. Repeat the procedure with turpentine oil also. I. For finding ‘l’: Determine the pitch and least count of scale of the spherometer. Place the spherometer on the dried surface of the convex lens. Turn the screw downwards very gently till the tip of the screw just touches the lens. Read and record the reading.

Keep the spherometer’s legs on the base of a paper and adjusting the central screw, find the pricks A, B and C of the three legs of the spherometer. Join the centres of the three pricks and measure the lengths with the half-metre scale. Note the values of AB, BC and AC. 3? Fig: (a) to find focal length of convex lens (b) for the length of legs AB, BC, CA of the spherometer Fig: to find focal length of the plano concave lens 4? Observations Pitch of the spherometer= 1 cm Least count of the spherometer = 0. 01 cm Distance between the legs: (1) AB (2) BC (3) CA = 3 cm = 3 cm = 3 cm Table for calculation of ‘h’

S. No Initial No. of reading of complete the C. S. on rotations the convex lens (n) (a) 62 0 64 0 Final Additional h=n x Mean reading C. S div. pitch “h” of the c. s moved +mx on the L. C glass slab 6. 5 4 55. 5 60 0. 555 0. 5775 0. 6 1 2 5? To measure focal length f ‘ of convex lens Distance of needle tip from Area S. No Tip of the upper Upper between surface of the surface of lens and convex lens the plane plane mirror X1 mirror X2 Without 1 30. 5 31 liquid 2 36. 7 37. 2 With water 1 31. 4 31. 8 2 37. 5 38. 1 With oil 1 9. 4 9. 6 2 10. 4 10,6 Mean x= Focal length 30. 75 36. 5 31. 6 37. 8 9. 5 10. 5 f1= 33. 85 f2=34. 7 f3=10 CALCULATIONS Mean distance between two legs =3 cm Mean h = 0. 7557 cm To find the radius of curvature of the convex lens: 6? Measurement of refractive indices of water and turpentine oil 1) With water between the convex lens and the plane mirror: 2) With turpentine oil between the convex lens and the plane mirror Result The refractive index of water is µ1 = 1. 06552 The refractive index of turpentine oil is µ2 = 1. 22736 7? Precautions (i) The screw of the spherometer should be moved in one direction only to avoid backlash error.

The screw should be moved just to touch the surface of the convex lens or the glass slab. () (i) The parallax should be removed properly. (iv) The lens and the plane mirror should be properly cleaned. (v) The convex lens of large focal length should be used. (vi) The spherometer reading should be taken first on the surface of the convex lens and then on the glass slab. Sources of error: (i) () The distances x1 and x2 may not be measured correctly. The value of h and l may not be correct. (i) Parallax may not be removed properly. (iv) Backlash error may be acting on the spherometer. 8?