13

EXPT NO: 13.   R.I. OF LIQUID

Aim :        To determine the R.I. of a liquid (water) by using

1) concave mirror  2) convex lens and plane mirror.

Apparatus : Concave mirror, convex lens, plane mirror, retort stand, index pin, string, half meter scale, liquid (water), Spherometer, glass plate.

Ray diagrams :

Formulae :

1)    R.I. of liquid using concave mirror =

where  is the distance between pole of mirror and pin without liquid.

 is the distance between surface of water and pin.

2)         R.I. of liquid using convex lens and plane mirror.

where R is the radius of curvature of one surface of convex lens, f is the focal length of combination of convex lens and liquid lens (or piano - concave liquid lens, is formed between plane mirror and convex lens) and is the focal length of convex lens.

3)         Radius of curvature of one surface of convex lens.

 where a is average distance between two legs of Spherometer and h is sagitta of surface of convex lens in contact with liquid (water)

Procedure :                PART I : R.I. of Liquid using concave mirror :

      Keep the concave mirror on the horizontal surface, with its reflecting surface upwards.

      Fix index pin horizontally in a clamp with retort stand and keep its tip on vertical line through pole of mirror.

      Coincide tips of the index pin and its image, (a) Move the index pin up and down and remove the parallax between tips of the pin and its image seen in the concave mirror.

      Note the distance (R₁) between tip of index pin and pole of concave mirror using half meter scale.

      Take small quantity of water in concave mirror, lower the index pin and remove the parallax between its tip and tip of the image as seen through water. Note the distance (R₂) between tip of index pin and surface of the water using half meter scale.

      Using formula determine R.I. of liquid.

      Take three independent sets of (R₁) and (R₂).

PART II (A) : For focal length of convex lens using convex lens and plane mirror :

      Find the approximate focal length of given convex lens by focussing distant object on the screen and measure the distance between lens and screen which is approximate focal length of convex lens ((f₁))

      Place a plane mirror on the horizontal surface with its reflecting surface upwards.

      Place the convex lens on the plane mirror.

      Clamp the index pin in the clamp of retort stand and hold it horizontally above the lens at distance equal to its approximate focal length of convex lens.

      Bring the tip of pin at the vertical principal axis of the lens so that tip of pin appears touching the tips of its image.

      Move the index pin up and down and remove the parallax between tips of the index pin and its image.

      Measure the distance () between tip of pin and upper surface of lens by half meter scale.

      Also measure the distance () between tip of pin and surface of the plane mirror by removing the convex lens.

      By using formula   find the focal length of given convex lens.

PART II (B) :

For focal length of the combination

(A piano concave liquid lens is formed between plane mirror and convex lens) :

1)         Take a few drops of a transparent liquid (water) on the plane mirror and place the convex lens over it (with its same face above as before).

2)         Repeat the steps 6, 7 & 8 from Part II. (A)

3)         By using formula    find the focal length of the combination.

4)         Repeat the procedure for taking three independent readings of and

5)         Find the mean focal length (f) of the combination.

PART III :   Find the radius of curvature (R) of surface of convex lens in contact with water using Spherometer :

      Find the least count (L.C) of Spherometer.

      Keep the Spherometer with its three legs in contact with paper and press it so that impressions of the tips of the legs are obtained. Measure the distance between two legs and find the average distance 'a'.

      Keep the glass plate on the table. Place the Spherometer on it. Rotate the screw so that the tip and legs just touch the glass plate. Note down M.S.R. and C.S.R. of Spherometer, hence find total reading 'X.

      Keep the convex lens with its one surface on the glass plate and place the Spherometer on the lens. Rotate the screw of Spherometer till middle tip and legs are just in contact with lens. Note M.S.R. and C.S.R. of Spherometer. Hence calculate total readings 'Y'.

      Repeat the procedure of X and Y for two more independent readings for two different positions on glass plate and convex lens. Hence find mean of X and Y.

      Find sagitta (h) of one convex surface using formula h = | Y - X |

      Find the radius of curvature of given convex surface of convex lens using formula

Observations :

1)     Approximate focal length of given convex lens = f₁ =…………..cm

2)     L.C. of spherometer =

3)     Average distance between two legs of Spherometer  a =

Observation table :

Part (I) For R.I. of liquid

Obs. No	Distance between pin and mirror without liquid    cm	Distance between pin & surface of liquid    cm	R.I. of liquid	Mean R.I. of liquid
01
02
03

Part (II) - For focal length of convex lens ():

Obs. No	cm	cm	cm	Mean    cm
01
02
03

Part (II) - For focal length of convex lens (f):

Obs. No	cm	cm	cm	Mean f   cm
01
02
03

Part IV : For Sagitta of one surface (in contact with water) of convex lens (h)

Using sphereometer:

Object	Obs No	Main Scale reading A cm	Circular Scale reading B	C=BxL.C	Total reading T=A+Ccm	Mean reading cm	Sagitta
Plane Surface	01					X=…..
	02
	03
Convex lense  Surface	01					Y=…..
	02
	03

Calculations :

 Results :

1)    R.I. of given liquid using concave mirror

2)     R.I. of given liquid using a piano concave liquid lens formed between plane mirror and convex lens

Precautions :

      The tip of the pin should lie on the principal axis of concave mirror.

      The tip of pin, centre of mirror and centre of lens should be at the same height.

      While removing the parallax, the eye should be kept at a minimum distance of 30 cm from the index pin.

      Parallax should be removed between index pin and image of index pin.

      Take sufficient quantity of liquid in the concave mirror and also between convex lens and plane mirror.

      The liquid should be clean and transparent.

      The index pin should be clamped horizontally.

      The circular scale of Spherometer should be rotated in same direction to avoid back lash error.

J KL