1. Aim

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

2. Apparatus Used

• Travelling microscope with vernier scale
• Glass slab of uniform thickness
• White paper with a fine ink mark
• Spirit level
• Laboratory stand with clamps
• Clean piece of cloth
• Micrometer screw gauge (for measuring thickness of the slab)

3. Diagram

Fig.1: Experimental setup for determination of refractive index using a travelling microscope

4. Theory

When a ray of light passes from one medium to another, it bends or refracts according to Snell's law. The refractive index of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium.

In this experiment, we use a travelling microscope to measure the apparent shift in position of a mark when viewed through a glass slab. When we observe a mark through a glass slab, the mark appears to be raised due to refraction of light at the two parallel surfaces of the glass slab.

Consider a point object O placed below a glass slab of thickness t and refractive index μ. When viewed from above, the object appears to be at position I which is at a height t' from the bottom surface of the glass slab.

According to the laws of refraction:

For small angles of incidence and refraction, we can write:

Where:

• t = actual thickness of the glass slab
• t' = apparent thickness of the glass slab

The apparent thickness (t') is less than the actual thickness (t) of the glass slab. By measuring both these quantities using a travelling microscope, we can determine the refractive index of the glass slab.

5. Formula

The refractive index of the glass slab is given by:

Where:

• Real thickness (t) = Direct measurement of thickness using micrometer screw gauge or difference of microscope readings when focused on top and bottom surfaces of the glass slab
• Apparent thickness (t') = Difference between the microscope readings when focused on the mark directly and when focused on the mark through the glass slab

Alternative formula using the microscope readings:

Where:

• h₁ = Reading when microscope is focused on the mark directly
• h₂ = Reading when microscope is focused on the bottom surface of the glass slab
• h₃ = Reading when microscope is focused on the top surface of the glass slab

6. Procedure

1. Setup Preparation:
   • Place a sheet of white paper with a fine ink mark on the laboratory table.
   • Level the travelling microscope using the spirit level and adjusting screws.
   • Ensure the microscope tube can move smoothly in the vertical direction.
2. Measurement of Direct Reading (h₁):
   • Focus the microscope on the ink mark on the paper.
   • Note the reading on the vertical scale of the microscope (h₁).
3. Placement of Glass Slab:
   • Clean the glass slab with a soft cloth to remove any dust or fingerprints.
   • Place the glass slab carefully over the mark, ensuring the slab is perfectly horizontal.
4. Measurement of Bottom Surface Reading (h₂):
   • Focus the microscope on the bottom surface of the glass slab.
   • Note the reading on the vertical scale (h₂).
5. Measurement of Top Surface Reading (h₃):
   • Move the microscope upward and focus it on the top surface of the glass slab.
   • Note the reading on the vertical scale (h₃).
6. Measurement of Mark Through Glass (h₄):
   • Without disturbing the glass slab, focus the microscope on the ink mark as seen through the glass slab.
   • Note the reading on the vertical scale (h₄).
7. Measurement of Glass Thickness:
   • Calculate the real thickness of the glass slab: t = h₃ - h₂
   • Calculate the apparent thickness: t' = h₄ - h₂
8. Repeat Measurements:
   • Repeat the above steps at least 5 times by focusing on different portions of the mark.
   • Record all readings in the observation table.

7. Observation Table

Least count of the travelling microscope = ________ mm

Thickness of glass slab measured by micrometer screw gauge = ________ mm

8. Calculations

For each observation:

1. Calculate the real thickness of the glass slab (t):

   t = h₃ - h₂

2. Calculate the apparent thickness (t'):

   t' = h₄ - h₂

3. Calculate the refractive index (μ):

   $\mu = \frac{t}{t'} = \frac{h_3 - h_2}{h_4 - h_2}$

Calculate the mean value of refractive index:

9. Result

The refractive index of the given glass slab is μ = _________ (with appropriate significant figures)

Standard value of refractive index for glass = 1.5

Percentage error = $\frac{|\text{Experimental Value} - \text{Standard Value}|}{\text{Standard Value}} \times 100\%$ = __________%

10. Precautions

1. The travelling microscope should be perfectly vertical and its movement should be smooth.
2. The glass slab should be placed perfectly horizontal on the paper with mark.
3. The glass slab should be clean and free from dust and fingerprints.
4. The ink mark should be fine and clear.
5. There should be proper illumination for clear focusing.
6. Parallax error should be avoided while taking the readings.
7. Focus the microscope carefully to get sharp images of the mark and the surfaces.
8. Avoid touching the optical surfaces of the microscope lens.
9. The reading should be taken without disturbing the setup.
10. The microscope should be focused by moving it in one direction only to avoid backlash error.

11. Sources of Error

1. Non-parallel faces of the glass slab can lead to distorted images.
2. Imperfect focusing of the microscope can lead to incorrect reading.
3. Presence of dust or fingerprints on the glass slab can affect the results.
4. Non-uniform thickness of the glass slab can lead to variations in measurements.
5. Improper leveling of the travelling microscope can cause systematic errors.
6. Parallax errors while taking readings from the scale.
7. Backlash error in the microscope movement.
8. The mark might not be perfectly visible through the glass slab due to multiple reflections.
9. Temperature variations can affect the refractive index of the glass.
10. Human errors in reading the vernier scale.

12. Viva Voice Questions