To Determine Refractive Index Of A Glass Slab Using Travelling Microscope

To determine refractive index of a glass slab using travelling microscope

Edited By Vishal kumar | Updated on Jul 02, 2025 07:29 PM IST

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.

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Aim
Apparatus
Theory
Diagram
Procedure
Calculation
Result
Solved Examples Based on Determining Refractive Index of a Glass Slab Using Travelling Microscope
Summary

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.

Frequently Asked Questions (FAQs)

1. How does this method of determining refractive index compare to other methods?

This method, using a travelling microscope, is relatively simple and direct. It allows for the measurement of refractive index without needing to measure angles of refraction directly. Other methods include the prism method (measuring the angle of minimum deviation), Brewster's angle method (finding the polarizing angle), and critical angle method (using total internal reflection). Each method has its advantages, but the travelling microscope method is particularly good for transparent slabs and provides a hands-on understanding of refraction.

2. Why is a travelling microscope used in this experiment instead of a regular microscope?

A travelling microscope is used because it allows precise measurement of vertical distances. It has a movable stage that can be adjusted vertically with high accuracy, typically to fractions of a millimeter. This precision is crucial for measuring the apparent shift in position caused by the glass slab, which is often quite small.

3. How does the precision of the travelling microscope affect the accuracy of the refractive index calculation?

The precision of the travelling microscope directly affects the accuracy of the refractive index calculation. The microscope's ability to measure small vertical displacements (typically to 0.01 mm or better) allows for precise measurement of the apparent shift caused by the glass slab. Higher precision in these measurements leads to a more accurate calculation of the refractive index. However, the overall accuracy also depends on other factors like the uniformity of the glass slab and the care taken in focusing.

4. How does the clarity of the glass slab affect the measurements?

The clarity of the glass slab is important for accurate measurements. A very clear, transparent slab allows light to pass through with minimal scattering or absorption, making it easier to focus precisely on the object beneath it. If the glass is slightly cloudy or has impurities, it might scatter light, making it harder to get a sharp focus and potentially affecting the apparent depth measurement.

5. Why is it important to ensure that the travelling microscope's movement is perfectly vertical?

Ensuring the travelling microscope's movement is perfectly vertical is crucial because any deviation from vertical would introduce errors in the depth measurements. If the microscope moves at an angle, the measured vertical displacement would be less than the actual displacement, leading to an incorrect calculation of the refractive index. Most travelling microscopes have leveling screws to adjust their orientation and ensure vertical movement.

6. How does the surface roughness of the glass slab affect the experiment?

The surface roughness of the glass slab can affect the experiment by scattering light as it enters and exits the slab. Ideally, the surfaces should be very smooth (optically flat) to minimize scattering and ensure that light paths are as predictable as possible. Rough surfaces can lead to diffuse reflection and refraction, making it harder to focus precisely and potentially affecting the apparent depth measurement.

7. What is the relationship between the real depth and apparent depth in this experiment?

The relationship between real depth (d) and apparent depth (d') is given by the equation: n = d/d', where n is the refractive index of the glass slab. This means that the real depth is always greater than the apparent depth, and the ratio between them gives us the refractive index.

8. What is the significance of the apparent depth in this experiment?

The apparent depth is the key measurement in this experiment. It represents the distance between the actual position of an object beneath the glass slab and where it appears to be when viewed through the slab. This apparent shift in position is directly related to the refractive index of the glass and forms the basis for calculating it.

9. Why is it important to measure the thickness of the glass slab at multiple points?

Measuring the thickness of the glass slab at multiple points is important because real glass slabs may not have perfectly uniform thickness. By taking measurements at several points and averaging them, we can get a more accurate representation of the slab's overall thickness. This average thickness is then used in the calculations, helping to minimize errors that could arise from thickness variations.

10. How does the shape of the glass slab affect the experiment?

The ideal shape for the glass slab in this experiment is a perfect cuboid with parallel faces. This ensures that light enters and exits the slab perpendicular to its surfaces when the slab is placed horizontally. If the slab were wedge-shaped or had curved surfaces, it would complicate the path of light through the glass and make the calculations more complex or potentially inaccurate.

11. How does the quality of the glass slab affect the accuracy of the experiment?

The quality of the glass slab is crucial for accurate results. Ideally, the slab should have uniform thickness, be free from bubbles or impurities, and have perfectly parallel faces. Any deviations from these ideal conditions can cause light to refract unpredictably, leading to errors in the apparent depth measurement and calculated refractive index.

12. What would happen if we used a glass slab with a very high refractive index?

Using a glass slab with a very high refractive index would result in a larger apparent shift in the position of the object. This could make the effect more noticeable and potentially easier to measure. However, it might also increase the likelihood of total internal reflection occurring if light hits the bottom surface of the slab at a sufficiently large angle. Very high index materials might also be more dispersive, potentially causing chromatic effects if white light is used.

13. What role does Snell's law play in this experiment?

Snell's law is the fundamental principle underlying this experiment, although we don't use it directly in its familiar form (n1 sin θ1 = n2 sin θ2). In this case, we're using light at normal incidence (θ = 0°), which simplifies Snell's law. The relationship between real and apparent depth (n = d/d') that we use is actually derived from Snell's law under these conditions. Understanding Snell's law helps explain why the light bends and why we see the apparent shift in position.

14. How does the concept of optical path length relate to this experiment?

Optical path length is the product of the physical path length and the refractive index of the medium. In this experiment, the optical path length through the glass slab is greater than the physical thickness of the slab. This increased optical path length is what causes the apparent shift in position of the object. Understanding optical path length helps explain why the object appears closer to the surface than it actually is.

15. What would happen if we used a glass slab with a gradient refractive index?

If we used a glass slab with a gradient refractive index (where the refractive index varies within the material), the path of light through the slab would be curved rather than straight. This would complicate the apparent depth measurement and make the standard calculation method inaccurate. Gradient index materials can cause light to follow complex paths, which would require more sophisticated analysis to determine an effective refractive index.

16. How does the concept of optical density relate to the refractive index in this experiment?

Optical density is directly related to refractive index. Materials with higher optical density generally have higher refractive indices. In this experiment, the glass slab has a higher optical density than air, which is why light slows down and bends when entering it. The greater the difference in optical density between the air and the glass, the more pronounced the apparent shift will be, making the effect easier to measure.

17. Why is it important to clean the glass slab before the experiment?

Cleaning the glass slab is crucial because any dirt, dust, or fingerprints on its surface can affect the path of light through the slab. These impurities can cause scattering or additional refraction, leading to inaccurate measurements of the apparent depth and, consequently, errors in the calculated refractive index.

18. Why is it important to ensure the glass slab is perfectly horizontal during the experiment?

Ensuring the glass slab is perfectly horizontal is crucial because any tilt would change the effective thickness of the slab through which light travels. This would lead to incorrect measurements of the apparent depth and, consequently, errors in the calculated refractive index. A spirit level can be used to check and adjust the slab's orientation.

19. What is the significance of using a thin, opaque object (like a needle) as the target in this experiment?

A thin, opaque object like a needle is used because it provides a clear, well-defined point to focus on. The sharpness of the needle's tip or edge allows for precise focusing both with and without the glass slab in place. This precision is crucial for accurately measuring the apparent shift in position caused by the glass slab.

20. Why is it important to focus the microscope without parallax when taking measurements?

Focusing without parallax is crucial because parallax error can lead to inaccurate readings of the microscope's vertical position. Parallax occurs when the observer's line of sight is not perpendicular to the scale being read. To avoid this, the microscope should be focused so that the crosshairs in the eyepiece appear stationary relative to the object when the observer's eye moves slightly.

21. How does the magnification of the travelling microscope affect the measurements?

The magnification of the travelling microscope doesn't directly affect the measurements, as we're interested in the vertical displacement rather than the size of the image. However, higher magnification can make it easier to focus precisely on the object, potentially improving the accuracy of the depth measurements. The key factor is the precision of the vertical movement mechanism, not the magnification.

22. How does the thickness of the glass slab affect the measurement of refractive index?

The thickness of the glass slab is directly proportional to the apparent shift in position of the object viewed through it. A thicker slab will cause a larger shift, while a thinner slab will cause a smaller shift. The refractive index calculation takes this thickness into account, so accurate measurement of the slab's thickness is crucial for determining the correct refractive index.

23. What are the main sources of error in this experiment?

The main sources of error include: 1) Inaccurate measurement of the glass slab thickness, 2) Imprecise focusing of the microscope on the object and its image, 3) Parallax error when reading the microscope scale, 4) Non-uniformity in the glass slab's thickness or composition, and 5) Errors in maintaining the microscope perpendicular to the glass surface.

24. How does temperature affect the refractive index measurement?

Temperature can affect the refractive index of materials, including glass. As temperature increases, the density of the glass typically decreases slightly, which in turn decreases its refractive index. While the effect is usually small for moderate temperature changes, it's important to note the temperature at which the experiment is conducted for precise measurements.

25. How does the angle of incidence affect the determination of refractive index in this experiment?

In this experiment, we typically use normal incidence, meaning the light enters the glass slab perpendicular to its surface. This simplifies the calculations because the angle of incidence is 0°. If the angle of incidence were not normal, it would complicate the calculations and require additional measurements to determine the refractive index accurately.

26. How does the refractive index of air affect the measurements in this experiment?

The refractive index of air is very close to 1 (approximately 1.0003 at room temperature and standard pressure). In most cases, it's assumed to be exactly 1 for simplicity. However, for extremely precise measurements, the slight difference from 1 can be taken into account, especially if the experiment is conducted under non-standard conditions.

27. What is the principle behind determining the refractive index of a glass slab using a travelling microscope?

The principle is based on the apparent shift in position of an object when viewed through a transparent medium. When light passes through the glass slab, it bends (refracts), causing objects beneath the slab to appear closer to the surface than they actually are. By measuring this apparent shift and the thickness of the slab, we can calculate the refractive index using Snell's law.

28. How does the wavelength of light affect the refractive index measurement?

The refractive index of a material varies slightly with the wavelength of light used. This phenomenon is called dispersion. In this experiment, we typically use white light, which is a mixture of all visible wavelengths. For more precise measurements, monochromatic light (light of a single wavelength) can be used, and the refractive index will be specific to that wavelength.

29. How does the refractive index of the glass slab relate to the speed of light in the glass?

The refractive index (n) of a material is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the material (v). Mathematically, n = c/v. This means that a higher refractive index corresponds to a lower speed of light in the material. In the glass slab, light travels slower than in air, which causes the bending of light rays and the apparent shift in position we observe.

30. How does the concept of total internal reflection relate to this experiment?

While total internal reflection doesn't directly occur in this experiment (as we're looking at light entering the glass from air, not vice versa), understanding it helps appreciate why the light bends as it does. Total internal reflection occurs when light tries to exit a medium with a higher refractive index (like glass) into one with a lower index (like air) at an angle greater than the critical angle. This phenomenon is the reason why the apparent position of the object shifts – the light bends towards the normal when entering the glass, causing the shift we measure.

31. What would happen if we used a liquid instead of a glass slab in this experiment?

If we used a liquid instead of a glass slab, the principle of the experiment would remain the same, but there would be some practical differences. Liquids typically have lower refractive indices than glass, so the apparent shift might be smaller. Additionally, containing the liquid without distortion and ensuring a uniform thickness would be more challenging. The surface of the liquid might also not be as perfectly flat as a glass slab, potentially introducing errors.

32. What would happen if we used a glass slab with a refractive index very close to that of air?

If we used a glass slab with a refractive index very close to that of air (which is approximately 1), the apparent shift in position would be very small. This would make the measurements more challenging and potentially less accurate, as the difference between the real and apparent depths would be minimal. In practice, most glasses have refractive indices significantly higher than air (typically 1.5 or more), making the effect more noticeable.

33. Why is it important to focus on the same point of the object with and without the glass slab?

Focusing on the same point of the object with and without the glass slab is crucial for accurate measurement of the apparent shift. If different points were focused on, it would introduce an error in the depth measurement. Using a distinct feature of the object (like the tip of a needle) helps ensure consistency in focusing. This consistency is key to accurately determining the difference between the real and apparent depths.

34. How does the wavelength dependence of refractive index (dispersion) affect this experiment?

Dispersion, the variation of refractive index with wavelength, can affect this experiment if white light is used. Different wavelengths will refract slightly differently, potentially causing a small spread in the apparent position of the object. This effect is usually small for glass in the visible spectrum, but for very precise measurements, using monochromatic light (like from a sodium lamp) can eliminate this source of uncertainty.

35. Why is it important to wait for the travelling microscope to stabilize before taking readings?

Waiting for the travelling microscope to stabilize before taking readings is important to avoid errors caused by mechanical vibrations or thermal expansion. When the microscope is moved, it may take a moment for all parts to settle into their final position. Additionally, touching the microscope can transfer body heat, causing slight thermal expansion. Waiting ensures that these effects have subsided, allowing for more accurate and consistent readings.

36. What would happen if we used a glass slab with internal stress or strain?

If we used a glass slab with internal stress or strain, it could exhibit birefringence, where the refractive index varies depending on the polarization and direction of light. This could cause the apparent position of the object to shift differently for different polarizations of light, complicating the measurements. In severe cases, it might even cause double images. For accurate results, it's important to use a glass slab that is as free from internal stresses as possible.

37. How does the accuracy of thickness measurement of the glass slab affect the final result?

The accuracy of the thickness measurement of the glass slab directly affects the final result because the thickness is used in the calculation of the refractive index. If the thickness measurement is off, it will lead to a proportional error in the calculated refractive index. For example, if the thickness is measured 1% too high, the calculated refractive index will be about 1% too high. This is why it's crucial to measure the thickness as accurately as possible, often using micrometers or other precision instruments.

38. Why is it important to ensure that the glass slab and the object are not moved during the experiment?

Ensuring that the glass slab and the object are not moved during the experiment is crucial for accurate measurements. Any movement would change the