Experiment 8 : To find the refractive index of a liquid using a concave mirror and a plane mirror.
AIM :
To find the refractive index of any liquid (water) using a concave mirror.
APPARATUS :
A concave spherical mirror, water, an optical needle, a clamp stand, one meter scale, plumb line, etc.
THEORY :
If the tip of object needle $O$ is at the centre of curvature $C$, the tip of the image will exactly coincide with it. ( Principle axis is verticle to the plane ).
When water is filled in the concave mirror, the object needle is moved to a new position $C'$ to remove the parallax between the tips of the object needle and its image.
A ray starting from $C$ reaches $E$ without deviation because it is along the radius of curvature. Due to water in the concave mirror the position of object and image shifts to $C'$.i.e now ray starting from $C'$ after refraction moves along $ED$ and then $DC$ to make the apparent centre of curvature.
$\angle NDC'=i \text{(incidence angle)}=\angle BC'D$
$\angle MDE =r \text{(refraction angle )}=\angle BCD$
${}^a\mu_w=\frac{\sin i}{\sin r}=\frac{\text{DB}/\text{DC}'}{\text{DB}/\text{DC}}=\frac{\text{DC}}{\text{DC}'}$
In $\triangle BC'D$,
$\sin i = \frac{\text{DB}}{\text{DC}'}$
In $\triangle BCD$,
$\sin r = \frac{\text{DB}}{\text{DC}}$
For normal view, D will be near B.
Therefore,
${}^a\mu_w = \frac{\text{BC}}{\text{BC}'}$
If small quantity of water in concave mirror, B will be very near to P, i.e.,
$\text{BC} \simeq \text{PC} \quad \text{and} \quad \text{BC}' \simeq \text{PC}'$
${}^a\mu_w =\frac{\text{PC}}{\text{PC}'}= \frac{\text{Real radius of curvature of mirror}}{\text{Apparent radius of curvature of mirror}}$
PROCEDURE :
1. Place the concave mirror on a horizontal surface ( plane ) so that its principal axis is along vertical.
2. Hold the optical needle horizontally in a clamp stand so that its tip lies just above the pole $P$ and at a distance approximately $2f$.
3. Remove the parallax between the needle and its image.
4. Mark the real and inverted image of the optical needle in the mirror and note the reading this image.
5. Measure the distance $PC$ using a plumb line and meter scale.
6. This measured distance is the actual radius of curvature of the concave mirror.
7. Now Add a small quantity of water into concave mirror which will change the position of image needle.
8. Adjust the screw to upper or lower optical needle and adjust it's position from 'C' to 'C' to remove parallex between the needle and it's shifted image is seen.
9. Measure $PC'$, the apparent radius of curvature.
10. Repeat the experiment 4–5 times and record the readings.
OBSERVATION TABLE
| SN | Real Depth (cm-R) | Apparent Depth (cm-R') | μ = R/R' |
|---|---|---|---|
| 1 | 28 | 22 | 28/22 = 1.27 |
| 2 | 30 | 24 | 30/24 = 1.25 |
| 3 | 32 | 26 | 32/26 = 1.23 |
CALCULATIONS :
Putting the observed values of actual radius R and apparent radius $R'$ in formula
Use the formula:
$\mu = \frac{R}{R'}$
Mean = (1.27 + 1.25 + 1.23) / 3 = 3.75 / 3
Mean= 1.25
Mean Refractive Index: $\mu = 1.25 $
RESULT
The refractive index of water, $\mu = 1.25$
PRECAUTIONS
1. The mirror and water surface should be clean.
2. The optical needle must be perfectly horizontal.
3. Parallax should be removed carefully.
SOURCES OF ERROR :
1. The needle may not be properly horizontal.
2. Parallax may not be fully removed.