## Aim/Aim of Experiment

To find the Refractive Index of a Liquid by using Convex

Lens and Plane Mirror.

## Apparatus/Material Required

- Convex lens
- A Plane mirror
- An optical Needle
- The clean transparent Liquid in beaker
- An Iron stand with base and clamp arrangement
- Pump line
- A plane glass slab
- A spherometer
- A half meter scale

## Theory

Let us consider f_{1} and f_{2} are the focal lengths of glass convex lens and liquid lens respectively, Let F be the focal length of their combination then,

1/F=1/f_{1}+1/f_{2} or 1/f_{2}=1/F-1/f_{1}

The Liquid lens formed is a plano-concave lens with R_{1}=R, and R_{2}=∞.

So, from lens maker’s formula,

1/f_{2}=(n-1)[1/R_{1}-1/R_{2}]

we have 1/f_{2}=(n-1)/R,

If R be the radius of curvature of the concave lens which is in contact with the liquid then the refractive index of the liquid is, n=1+R/f_{2}.

Where n is the refractive index of the liquid and by putting the value of f_{2} then n can be calculated.

## Diagram

## Procedure

**For the Focal length of Canvex lens:**

- Take a convex lens and find its rough focal length.
- Place the plane mirror horizontally on the base of the iron stand with its reflecting surface upward and place the convex lens on the plane mirror.
- Tight the screw of optical needle in the clamp of the stand and hold it horizontally above the lens at distance equal to its rough focal length.
- For the tip of the needle appears touching the tip of its image, bring the tip of the needle at the vertical principal axis of the lens.
- To remove parallax between tips of the needle and its image, move the needle up and down, so that image and object will be the same size.
- Measure the distance between tip and upper surface of the lens by using a plumb line and half metre scale, also measure the distance between tip and the surface of its plane mirror.

**For the Focal length of the combination:**

- Firstly remove the lens and take few drops of the given transparent liquid on the plane mirror.
- Now place the convex lens over the liquid with its same face in cantact with the liquid above as before.
- Repeat the Steps 5 and 6 of the above.
- Record your observations.

**For the radius of curvature of convex lens surface:**

- A plano-concave lens formed between the convex lens and the plane mirror so radius will be R
_{1}=R, and R_{2}=∞. - From lens maker’s formula 1/f2=(n-1)[1/R
_{1}-1/R_{2}becomes 1/f_{2}=(n-1)/R. - Now the radius of curvature of the Canvex lens can be calculated by the formula R=(n-1)f
_{2}, where n is the refractive index of the liquid.

## Observations

1. The rough focal length of the convex lens = 35 cm.

2. Table for distance of needle tip from Lens and Mirror:

Arrangement | Distance of needle tip from lens surface x_{1} (cm) | Distance of needle tip from plane mirror x_{2} (cm) | Distance of needle tip Mean [x=(x_{1}+x_{2})/2] | Focal Length x (cm) |
---|---|---|---|---|

(1) | (2a) | (2b) | (2c) | (3) |

Without Liquid | 34.5 | 35 | 34.75 | f_{1}=34.75 |

With Liquid | 51.5 | 49 | 50.25 | F=50.25 |

3. The Radius of curvature of the Convex lens surface = 70 cm.

## Calculations

**1. Calculation for the focal length of liquid lens:**

1/f_{2}=1/F-1/f_{1},

putting the value of F and f_{1},

So, 1/f_{2} = 1/34.75-1/50.25

=0.02878-0.01990

1/f_{2} = 0.00888,

Hence, f_{2}=1/0.00888 = 112.612.

**2. Calculation for the refractive index of the liquid:**

n=1+R/f_{2},

putting the value of R and F_{2},

n=[1+(70/112.612)]

= 1+0.6216

Hence, n = 1.6216.

## Result

The refractive index of the liquid is, n=1.6216.

## Precautions

- The liquid taken should be clean and transperant.
- The layer of liquid not be thick, so only a few drops of liquid should be taken.
- The parallax should be removed tip to tip.

## Sources of Error

- The taken liquid not be quite transperant.
- The parallax may not be fully removed.

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