Refractive index of a glass slab by a travelling microscope

Introduction

The index of refraction, also called the refractive index, is a measurement of how much a ray of light bends as it passes through one medium and into another. If ’i’  is the angle of incidence for a ray in the vacuum (the normal is the angle formed by the incoming ray and the perpendicular to the medium’s surface), and ‘r’ is the angle of refraction(the angle between the ray in the medium and the normal). 

The refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction ; n = sin i / sin r. The velocity of light c of a particular wavelength in empty space divided by its velocity v in a substance, or n = c/v, is the refractive index.

A vertically mounted compound microscope is known as a travelling microscope. It has a vernier scale that may be moved up and down along with the main scale. A glass slab is a substance or sheet formed of glass that is cuboidal in shape and has three dimensions: length, width, and height. It doesn’t divert or scatter the light beams that travel through it. 

The incident and emergent rays originating from the glass slab are therefore parallel. Only a lateral or (sideways) shift or displacement in the direction of light is produced by the glass slab.

Refractive index of a glass slab using a travelling microscope

Required materials for the same:

• Three different-thickness glass slabs made of the same material
• A portable microscope
• powdered lycopodium

The idea behind a glass slab

Due to the phenomenon of refraction, when a glass slab is placed in the air on a horizontal surface, and its bottom side is viewed from above, it appears to be elevated. The gap between this seeming bottom and the actual bottom, the apparent thickness of the slab, is determined by the top surface of the slab.

When a glass slab is put on a horizontal surface, and the bottom surface is viewed from above, it seems to be elevated owing to refraction. The distance between the apparent bottom and top of the glass slab determines the apparent thickness of the slab. The refractive index of the medium and air is calculated as follows:

n = real thickness of the slab/apparent thickness of the slab

Series of steps:

• Place the moving microscope (M) close to the window to gather enough light.
• Adjust the levelling screw to make the microscope’s base horizontal.
• Adjust the location of the eyepiece for clear visibility of the cross wire.
• Determine the vernier constant for the microscope’s vertical scale.
• Using black ink, mark point P on the microscope’s base.
• Make the microscope vertical and focus on P to avoid parallax between the cross-wires and the mark P.
• Let R1 be the vernier scale and the vertical scale’s primary scale reading.
• Over the mark P, place the glass slab with the least thickness.
• Let P1 be the cross mark’s image. Focus the microscope on P1 by moving it upwards.
• Measure R2 on the vertical scale, R2 on the reading scale
• Sprinkle a few lycopodium powder particles on the slab’s surface.
• Raise the microscope further higher to bring the particle closer to S.
• Measure R3 on the vertical scale, R3 on the reading scale,
• For varied thicknesses of glass slabs, repeat the processes above.
• Keep a journal of your findings.

Real thickness = R3-R1

Apparent thickness = R3-R2

Refractive index n = R3 – R1/R3 – R2

The ratio R3- R1/R3- R2 determines the refractive index of the glass slab.

Major precautions to be taken

• In a microscope, the parallax should be appropriately removed.
• The microscope should be adjusted upward to avoid backlash errors.

Error-Producing Sources

• It’s possible that the microscope’s scale isn’t properly calibrated.
• The layer of lycopodium powder on the glass slab could be quite thick.

• The refractive index of glass is 1.5.

Normal Shift:

A normal shift is an apparent shift in the position of an object placed in one medium and observed along the normal from the other medium. A normal shift occurs when an object and an observer are in distinct media, and the object’s image appears to have been displaced from its original position.

The normal shift is determined by the thickness and refractive index of the refracting material.

The apparent shift of a ray is the perpendicular distance between the incident and emerging rays as measured by light refraction through a glass slab. When different torques exist and are balanced by the box being level on the ground, the normal force shifts.

Consider the case of a box on a frictionless surface. To balance gravity, the normal force must act through the centre of mass when it is stationary. Now, from one of the top sides, push the box sideways. Because the push is above the centre of mass, torque is created. Gravity is incapable of restoring torque. Instead, we analyse the normal force operating at a place that generates enough torque to result in zero total torque.

Metre is the SI unit for normal shift. The emergent ray changes laterally when a ray of light strikes a parallel-sided glass slab obliquely. “Lateral shift” refers to the perpendicular distance between the incident and emerging ray directions.

Apparent Shift

When an object is placed in one medium and observed through another, the observer’s image and the object are in distinct places. Note that when an object is in a denser medium, the picture shifts towards the boundary, and when the object is in a less dense medium, the image moves away from the boundary.

The following are the factors that influence apparent depth:

1. The medium’s nature
2. Medium’s thickness
3. The hue of light

Measurement of refractive index

The refractive index of a medium is measured with a refractometer. Refractometers come in a variety of shapes and sizes, including the Abbe refractometer. The theory behind a refractometer is that light bends when it enters a different medium. The angle of refraction of light rays travelling through an unknown substance is measured with this equipment. By applying Snell’s law, this measurement, along with knowledge of the refractive index of the medium directly in contact with the unknown sample, is used to determine the refractive index of the unknown sample.

Why is it necessary to calculate refractive indices?

Refractive indices serve a variety of applications, but they are most commonly employed to distinguish between liquid samples. As a result, in the same way, as melting points are used to characterise solids, this physical quantity is utilised to characterise liquids. By comparing a substance’s refractive index to known literature values, this measurement can be used to identify it. Furthermore, by comparing the refractive index of a substance to that of a pure compound, refractive indices can be used to assess the purity of a chemical.

By comparing the solution’s refractive index to a standard curve, refractive indices can also be used to determine the concentration of a solute in a solution. Finally, the polarizability of a material affects refractive indices. The higher a substance’s refractive index, the more polarizable it is. As a result, knowing a substance’s refractive index is also required to compute its dipole moments.

Conclusion

The refractive index is affected by the following factors:

Temperature

• The refractive index is commonly calculated at room temperature.
• When a liquid is heated to a higher temperature, it loses its thickness and viscosity, allowing light to quickly pass through it. The refractive index has a lower value as a result of the lowered ratio.
• At lower temperatures, the liquid becomes denser and has a higher viscosity, causing light to travel slower across the medium. The refractive index has a higher value as a result of the larger ratio.
• Temperature regulation is commonly included in refractometers.

Light’s wavelength

• Because different wavelengths interfere with the atoms of the medium to varying degrees, the refractive index varies linearly with wavelength.
• Monochromatic light is essential for preventing light dispersion into distinct colours.
• The medium should not absorb the given wavelength.
• The most commonly utilised wavelength of light for a refractometer is the sodium D line at 598 nm.