Determining the Refractive Index of a Glass Slab using a Traveling Microscope

The Refractive index of any material is a dimensionless number that decides how fast light would travel in that material. Refractive index can also be defined for objects that are considered opaque because even if the light of visible frequency cannot pass through it, the light of much higher frequency like gamma rays or x-rays can pass through them, and the refractive index may be calculated with respect to that. The Refractive index is always calculated with respect to another medium. It may even be a vacuum, but most commonly, it is air because air is the most pervasive and ubiquitous medium on earth and the sunlight enters the earth through the air every day.

The formula for calculating the refractive index is the ratio of the velocity of light in both media. The numerator is the medium we desire to calculate the refractive index, and the medium for which the refractive index is defined is the denominator. If the reference medium is taken to be a vacuum, then the formula for refractive index becomes:

n = cv

Here,

n is the refractive index

c is the speed of light in a vacuum

v is the speed of light in the medium of which the refractive index is to be calculated

If we take the example of water, then we see that light travels 1.33 times slower in water than in air. This means that the refractive index of water is 1.33 with respect to water. The Refractive index of a material is inversely proportional to the speed of light in that medium. The greater the refractive index, the slower light travels through that material. The difference in speed is manifested as the distortion of the path of light when it enters the medium. The direction of the light wave turns through an angle upon entering. This makes the perception of objects through a refractive medium distorted, and the apparent distance of objects through them is not true. If the refractive index of media is the same, then the light wave does not show any divergence from its path, as the speed of light in both media is the same.

The reason why the light wave shows a divergence from its path is the principle of conservation of momentum. Packets of light called photons have mass and momentum associated with it. When the photons enter a different medium, the speed of the photon particles is altered. Now, momentum is defined as the product of mass and velocity, so if the velocity changes, the momentum has to be transferred somewhere to conserve it between the system. This is done by the wave changing the directional momentum. Therefore, the direction of light upon entering the medium changes. Snell’s law gives the angle through which the light will diverge from its path. Snell’s law states that the equation relates the angles of incidence and refraction:

n₁sinθ₁ = n₂sinθ₂

Here,

n₁ is the refractive index of the first medium

n₂ is the refractive index of the second material

θ₁ is the angle of incidence

θ₂ is the angle of refraction

Using the above equation, we can calculate the refractive index of any material if the angle of incidence and angle of refraction is accurately measured.

For a glass slab, the refractive index can be calculated by calculating the ratio between the actual thickness of the slab and the apparent thickness of the slab as seen through the slab. The refractive index becomes: n = real thickness of the slab/apparent thickness of the slab

Calculation of the refractive index of a glass slab can be done with the help of a travelling microscope. A travelling microscope is a type of microscope that can be adjusted to slide up and down a fixed scale that is provided with the main scale and a Vernier scale for accurate measurements.

Procedure

Take a piece of paper and make a mark on it with black ink.
Place this piece of paper under a travelling microscope.
Adjust the microscope so that the point on the paper is in sharp focus. This reading is r1.
Now, put a glass slab on the piece of paper and observe the same mark on it through the travelling microscope. Adjust it so that the mark is again in sharp focus. This reading is r2.
Put some talcum powder on the surface of the glass slab and adjust the microscope so that the particles of the powder are in sharp focus. This reading is r3.
Repeat the above steps for a few more readings.
Calculate the average of all the readings.

The refractive index can be calculated by applying the formula:

n = actual thickness of the slab/apparent thickness of the slab = (r₁- r₃)/(r₁ - r₂