To determine refractive index of a glass slab using travelling microscope

To determine the refractive index of a glass slab using a travelling microscope, we rely on the principle of refraction, which occurs when light passes from one medium to another, changing its speed and direction. The refractive index is a measure of how much light bends when entering the glass slab. In this experiment, we use a travelling microscope, a precision instrument that allows for accurate measurement of small distances. By placing the glass slab on a table and focusing the microscope on the upper and lower surfaces of the slab, we measure the apparent thickness of the slab (when viewed through the microscope) and its actual thickness. The refractive index of the glass slab can then be calculated using the ratio of the real thickness to the apparent thickness. This method is widely used because it provides an accurate and straightforward way to determine the refractive index, which is important in understanding the optical properties of materials.

Aim

To determine the refractive index of a glass slab using a travelling microscope.

Apparatus

Three "glass slabs of different thicknesses but the same material, a travelling microscope, and lycopodium powder. A slab is a piece of transparent material with rectangular faces. All faces are transparent and opposite faces are parallel. The dimension along with the light travels inside the slab is called its thickness.

A Short Description of a Travelling Microscope
It is a compound microscope fitted vertically on a vertical scale. It can be moved up and down, carrying a vernier scale moving along the main scale. In any position, the reading is taken by combining the main scale and the vernier scale reading.

Theory

$\mu=\frac{\text { Real thickess of the slab }}{\text { Apparent thickness of the slab }}$

Diagram

Procedure

Adjustment of the travelling microscope

1. Place the travelling microscope (M) on the table near a window so that sufficient light falls on it.
2. Adjust the levelling screws so that the base of the microscope becomes horizontal.

3. Make the microscope horizontal. Adjust the position of the eyepiece so that the cross wires are clearly visible.
4. Determine the vernier constant of the vertical scale of the microscope.

Other steps
5. Make a black-ink cross-mark on the base of the microscope. The mark will serve as point P.

6. Make the microscope vertical and focus it on the cross at P, so that there is no parallax between the cross-wires and the image of the mark P.
7. Note the main scale and the vernier scale readings (R₁) on the vertical scale.
8. Place the glass slab of the least thickness over the mark P.

9. Raise the microscope upwards and focus it on the image P₁ of the cross-mark
10. Note the reading P₂ on the vertical scale as before (Step 7 )
11. Sprinkle a few particles of lycopodium powder on the surface of the slab.

12. Raise the microscope further upward and focus it on the particle near S.
13. Note the reading R₃ on the vertical scale again (Step 7)
14. Repeat the above steps with another glass slab of more thickness.
15. Record your observations.

Calculation

Vernier constant (least count) for the vertical scale of microscope = .....

$\begin{aligned} & \mu=\frac{\text { Real thickess of the slab }}{\text { Apparent thickness of the slab }} \\ & \mu=\frac{R_3-R_1}{R_3-R_2} \\ & \text { Mean }=\mu=\frac{\mu_1+\mu_2+\mu_3}{3}\end{aligned}$

Result

The ratio $\frac{R_3-R_1}{R_3-R_2}$ is constant. It gives the refractive index of the material of the glass slab.

Solved Examples Based on Determining Refractive Index of a Glass Slab Using Travelling Microscope

Example 1: An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment, distances are measured by

1)a screw gauge provided on the microscope

2) a vernier scale provided on the microscope

3)a standard laboratory scale

4)a meter scale was provided on the microscope.

Solution:

A vernier scale is provided on the microscope.

Hence, the answer is the option (2).

Example 2: An experimenter wants to determine the refractive index (n) of a glass slab using a travelling microscope. The experimental setup is as follows:

Medium Refractive Index (n) Air Glass Slab 1.00?

The following measurements are recorded

Distance between the object pin and the objective lens (u) = 20.0 cm
Distance between the image pin and the objective lens (v) = 60.0 cm
Distance between the object pin and the glass slab (x) = 30.0 cm
Distance between the image pin and the glass slab (y) = 40.0 cm

Using the given data and the formula:

$n=\frac{v}{u} \cdot \frac{x}{y}$, calculate the refractive index (n) of the glass slab.

1)1.60

2)1.70

3)2.00

4) 2.25

Solution:

Given values:

u = 20.0 cm
v = 60.0 cm
x = 30.0 cm
y = 40.0 cm

The formula for calculating the refractive index of the glass slab is:

$
n=\frac{v}{u} \cdot \frac{x}{y}
$
Substituting the values into the formula:

$
n=\frac{60.0 \mathrm{~cm}}{20.0 \mathrm{~cm}} \cdot \frac{30.0 \mathrm{~cm}}{40.0 \mathrm{~cm}}
$

Calculating each part of the equation:

n = 3.0 * 0.75

n = 2.25

Rounded to three significant figures, the refractive index of the glass slab is approximately n = 2.25.

Therefore, the refractive index of the glass slab is n = 2.25.

Hence, the answer is the option (4).

Example 3: A student conducts an experiment to determine the refractive index (n) of a glass slab using a travelling microscope. The experimental setup is illustrated below:

Medium Refractive Index (n)

The student records the following measurements during the experiment:

Distance between the object pin and the objective lens (u) = 22.5 cm
Distance between the image pin and the objective lens (v) = 67.5 cm
Distance between the object pin and the glass slab (x) = 35.0 cm
Distance between the image pin and the glass slab (y) = 52.5 cm

Using the given data and the formula:

$n=\frac{v}{u} \cdot \frac{x}{y}$, calculate the refractive index (n) of the glass slab.

1) 2.00

2)1.70

3)1.85

4)2.20

Given values:

u = 22.5 cm
v = 67.5 cm
x = 35.0 cm
y = 52.5 cm

The formula for calculating the refractive index of the glass slab is:
$
n=\frac{v}{u} \cdot \frac{x}{y}
$
Substituting the values into the formula:

$
n=\frac{67.5 \mathrm{~cm}}{22.5 \mathrm{~cm}} \cdot \frac{35.0 \mathrm{~cm}}{52.5 \mathrm{~cm}}
$

Calculating each part of the equation:

n = 3.0 * 0.6667

n = 2.00001

Rounded to three significant figures, the refractive index of the glass slab is approximately n = 2.00.

Therefore, the refractive index of the glass slab is n = 2.00.

Hence, the answer is the option (1).

Example 4: A glass slab of known thickness $t=2 \mathrm{~cm}$ is placed on a horizontal platform. A travelling microscope is set up in such a way that it views the image of a distant object through the glass slab. The microscope is focused on the image without the glass slab. When the glass slab is placed, the microscope needs to be moved vertically upward by $h=0.5 \mathrm{~cm}$ to focus on the image again. Determine the refractive index $n$ of the glass slab.

1) $3 \cdot \sin i$
2) $4 \cdot \sin i$
3) $2 \cdot \sin i$
4) $3 \cdot \sin i$

Solution:

Step 1: The situation involves the glass slab acting as a medium with a certain refractive index n through which light passes.

Step 2: Consider the setup. When the microscope is focused on a distant object without the glass slab, the light travels through air (with refractive index $n_{\mathrm{air}}=1$).

Step 3: When the glass slab is placed on the platform, light travels through the glass slab (with refractive index n ) and then through air.

Step 4: By Snell's Law, we have:

$
n_{\text {air }} \sin i=n \sin r
$

where $i$ is the angle of incidence and $r$ is the angle of refraction inside the glass slab.
Step 5: Since $n_{\text {air }}=1$, we get:

$
\sin i=n \sin r
$
angled triangle.
Step 7: Using trigonometry, we have:

$
\tan r=\frac{h}{t}
$
Step 8: Substitute the value of $\tan r$ in terms of $h$ and $t$ into the equation from step 5:

$
\sin i=n \cdot \frac{h}{t}
$
Step 9: Solve for $n$ :

$
n=\frac{t \cdot \sin i}{h}=\frac{2 \mathrm{~cm} \cdot \sin i}{0.5 \mathrm{~cm}}=4 \cdot \sin i
$
So, the refractive index $(n)$ of the glass slab is $4 \cdot \sin i$.
Hence, the answer is the option (2).

Summary

In this experiment, we determine the refractive index of a glass slab using a travelling microscope. By measuring the real and apparent thickness of the slab with the microscope, we calculate the refractive index as the ratio of the real thickness to the apparent thickness. This experiment is significant in studying the optical properties of the glass, as the refractive index indicates how much light bends when passing through the material. The use of a travelling microscope ensures precise measurements, making this method reliable for determining the refractive index.