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Refractive Index is the ratio of speed of light in a vacuum to speed of light in the second medium of greater density. Refractive Index is commonly represented by the letter n. The index of refraction indicates the impact of material on the speed of light traveling through it. The refractive index can be calculated by the formula n = c/v.
Key Terms: Refractive Index, Refractive Index Formula, Refractive Index Examples, Refractive Index Gradient, Speed, Light
Refractive Index
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The refractive index is the ratio of the speed of light in a vacuum to the same in any given medium.
- When a ray of light travels from one medium to another, it changes its direction due to the differences in the speed of light in each medium.
- In a vacuum, light travels at 3 x 108 meters per second, but in air, it travels at 2.98 x 108 meters per second.
- When light travels through a medium other than a vacuum, the atoms in that medium absorb and then re-emit the light particles which reduces the speed of light.
- The properties of the medium influence the speed of light passing through it.
- In electromagnetic waves, the speed of light is determined by the optical density of the medium.
- The tendency of atoms in a substance to recover the absorbed electromagnetic energy is known as optical density.
- Higher the optical density of a substance, the slower the light passes through it.
The figure illustrates that when light passes from a material of refractive index n1 to material of refractive index n2, it bends from its initial path.
- If the light travels from an optically rarer medium to a denser medium, it bends towards the normal.
- If the light travels from an optically denser to a rarer medium, it bends away from the normal.
It is also important to note that the direction of the light changes when it travels from one medium to another. Hence, the refractive index of a medium can also be calculated using Snell’s Law.
Colors And Refractive Index
In a vacuum, all colors have similar velocities. However, when they pass from a vacuum into some other medium, their velocity changes. Therefore, colors also have different refractive indices.
The refractive index of colors varies with their different wavelengths. Violet color has the highest refractive index, therefore it travels the slowest and is at the bottom of a rainbow. On the other hand, the Red color has the lowest refractive index, hence travels the fastest and is at the top.
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Refractive Index Formula
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The Refractive index is a dimensionless quantity. The Refractive index is represented by the symbol n, or μ. It is the velocity of light in a vacuum divided by the velocity of light in a medium. The formula for refractive index is as follows:
n = \(c \over v\)
where,
- n is the refractive index
- c is the speed of light in a vacuum (3 × 108 m/s)
- v is the speed of light in the given medium
Factors that affect Refractive Index
The value of the refractive index is also affected by temperature and wavelength of light:
Temperature
Refractive index values are usually calculated at standard temperature.
- A higher temperature will make a liquid less dense and viscous, causing light to travel faster in that medium. This results in a smaller refractive index value for the refractive index due to a smaller ratio.
- A lower temperature will make a liquid denser and viscous, causing light to travel slower. This results in a larger refractive index value due to a larger ratio.
Wavelength of light
The refractive index varies linearly with wavelength as different wavelengths interfere to different extents with atoms of a medium.
- Monochromatic light should be used to prevent the dispersion of light into different colors.
- The chosen wavelength shouldn’t be absorbed by the medium.
Refractive Index Example
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Glass has a refractive index of 1.52 and the refractive index of water is 1.33.
- The speed of light in water is faster than the speed of light through glass as the glass has a greater refractive index than the refractive index of water.
- When one medium's refractive index is more than that of another, the first medium is said to be optically denser.
- The majority of substances we are familiar with have a refractive index that is greater than zero.
- When a material possesses negative permittivity and permeability, it will have a negative refractive index.
Types of Refractive Index
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There are mainly two types of Refractive Index that includes –
- Absolute Refractive Index
- Relative Refractive Index
Absolute Refractive Index
The Absolute Refractive Index is the refractive index in a vacuum. It refers to the ratio of velocity of light in vacuum to the velocity of light in a different medium.
Absolute Refractive Index (n) = c/v
where c refers to the speed of light in a vacuum and v is the speed of light in a medium.
Relative Refractive Index
The Relative Refractive Index refers to the ratio of velocity of light in a medium to velocity of light in another medium. It is basically the relative change in speed of light while traveling from one medium to another.
If we have two different mediums, A and B. The Refractive Index will be:
- Relative Refractive Index of Medium B = Refractive index of Medium B concerning that of Medium A.
Formula:
nBA = Velocity of Light in Medium A / Velocity of Light in Medium B
Similarly nAB = Velocity of Light in Medium B / Velocity of Light in Medium A
Refractive Index of Medium
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The refractive index of the Vacuum is 1. The higher the refractive index, the denser the medium is, and the slower the speed of light is. The Refractive index of some common mediums is given below in the table:
| Medium | Refractive Index |
|---|---|
| Air | 1.0003 |
| Water | 1.333 |
| Diamond | 2.417 |
| Ice | 1.31 |
| Ethyl Alcohol | 1.36 |
Why is High Refractive Index Important for Optical Polymers?
Optical polymers having high refractive index allow the rays of light to bend more within the material, that further helps in lowering the profile of the lens. Also, as the refractive index is increased, the thickness of the lens decreases, which results in less weight.
Refractive Index Gradient
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The rate of change of the refractive index with respect to distance in the material is known as the refractive index gradient.
- The slope of the refractive index profile at any point is referred to as distance.
- The reciprocal of a unit of distance is used to express the refractive index gradient.
- The rate of change of the refractive index with respect to distance is an example of a refractive index gradient.
- The refractive index gradient is a vector quantity.
Refractive Index and Wavelength
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According to the refractive index, the speed of light is the product of wavelength and frequency.
- The frequency of the light wave stays unchanged, irrespective of the medium.
- However, the wavelength of the light wave changes on the basis of refraction.
- Therefore, the refractive index varies with changes in wavelength.
Also Read:
| Ray Optics and Optical Instruments – Important Topics | ||
|---|---|---|
| Uses of Concave Mirror | Angle of Incidence | Derivation of Prism Formula |
| Optics | Mirror Formula | Periscope |
| Luminance | Fisheye Lens | Toric Lens |
Things to Remember
- Refractive Index is the ratio of the speed of light in a vacuum to the speed of light in any given medium.
- The speed of light in water is faster than the speed of light in glass.
- The Refractive index gradient is the rate of change of the refractive index with respect to distance in the material.
- The frequency of the light wave remains unchanged in every medium.
- The refractive index varies with wavelength.
Sample Questions based on Refractive Index
Ques 1: A lens behaves as a converging lens in air and a diverging lens in water (g = 4/3). What will be the condition on the value of the refractive index (g) of the material of the lens? (Delhi 2011C, 1 Mark)
Ans: A lens behaves as a converging lens in air and a diverging lens in water because the refractive index of the lens is less than the refractive index of water.
Ques 2: Under what condition, does a biconvex lens of glass having a certain refractive index act as a plane glass sheet when immersed in a liquid? (Delhi 2012, 1 Mark)
Ans: A biconvex lens of glass having a certain refractive index acts as a plane glass sheet when immersed in a liquid when the refractive index of the lens is equal to the refractive index of the liquid.
Ques 3: A converging lens of refractive index 1.5 is kept in a liquid medium having the same refractive index. What would be the focal length of the lens in this medium? (HOTS; Delhi 2008, 1 Mark)
Ans: Since the lens is placed in the same medium as that of the lens, the ray will pass without any deviation.
In liquid, \({1 \over f} = ({\mu_g \over \mu_s} - 1)({1 \over R_1} - {1 \over R_2})\)
Given, \(\mu_g = \mu_s\)
Therefore, \({1 \over f} = ({\mu_g \over \mu_g} - 1)({1 \over R_1} - {1 \over R_2}) = 0\ \)
or f = infinity
Ques 4: A biconvex lens made of a transparent material of refractive index 1.25 is immersed in water of refractive index 1.33. Will the lens behave as a converging or a diverging lens? Give a reason. (All India 2014, 2 Marks)
Ans: When a lens is placed in a liquid in which the refractive index is more than that of the material of the lens, then there is a change in the nature of the lens. So, when a biconvex lens of refractive index 1.25 is immersed in water (refractive index 1.33) its nature will change because it has a higher refractive index. So, a biconvex lens will act as a biconcave lens or diverging lens.
Ques 5: How does the focal length of a lens change when a red light incident on it is replaced by violet light? Give a reason for your answer. (All India 2012, 2 Marks)
Ans: The refractive index of a lens increases with the decrease in the wavelength of the incident light. So, the focal length will decrease with a decrease in wavelength.
\(\frac{1}{f}=(\mu - 1) \lgroup\frac{1}{R_1}-\frac{1}{R_2}\rgroup\)
Ques 6: The refractive index of diamond is much greater than that of glass. How does a diamond cutter make use of this fact? (All India 2011C, 2 Marks)
Ans: The refractive index of diamond is much higher than that of glass. Due to this, the critical angle for the diamond air interface is low. The diamond is cut suitably so that the light entering the diamond from any face suffers multiple internal reflections on all surfaces.
Ques 7: (a) Monochromatic light of wavelength 589 nm is incident from the air on a water surface. If p for water is 1.33, find the wavelength, frequency, and speed of the refracted light.
(b) A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm. (All India 2017, 2 Marks)
Ans: (a) Given: Wavelength of monochromatic
light, λ = 589 nm = 589 × 10-9m,
Refractive index of water, µ = 1.33,
Speed of light in air, c = 3 × 108 ms-1
Since the frequency of light does not depend on the property of the medium in which it is traveling. Hence, the frequency of the emergent ray in water is equal to the frequency of the incident or emergent light in air.
The relation between the speed of light in water to the refractive index of water can be given as:
The wavelength of light in water is given by the relation,
Ques 8: (a) Obtain lens makers formula using the expression
\({n_2 \over v_1} - {n_1\over u} = {n_2 - n_1 \over R_1}\)
(b) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the pole. Using this diagram, derive the magnification formula for the image formed. (Delhi 2011, 3 Marks)
Ans: (a) Lens maker’s formula: Consider a thin double convex lens of refractive index n2 placed in a medium of refractive index n1.
Here, n1 < n2.
Let B and D be the poles, C1 and C2 are the centers of curvature, and R1 and R2 as the radii of curvature of the two lens surface ABC and ADC, respectively.
For refraction at surface ABC, the relation between the object distance u, image distance v1, and radius of curvature R1 can be given as
\({n_2 \over v_1} - {n_1\over u} = {n_2 - n_1 \over R_1} - i)\)
For refraction at surface ADC, the relation between the object distance v1, image distance v, and radius of curvature R2 can be given as
(b) 
Ques 9: If the refractive index of diamond is 2.41, then what will be the speed of light passing through it? (2 marks)
Ans: Refractive index of diamond = speed of light in air/speed of light in the diamond
=> µdiamond = c / vdiamond
=> vdiamond = c / µdiamond = (3 x 108) / 2.41 m/s = 1.24 x 108 m/s
Ques 10: If the speed of light in water is 2.25 x 108, then what will be the refractive index of water? (2 marks)
Ans: airµwater = c / v = speed of light in air / speed of light in water
=> airµwater = ( 3 x 108) / (2.25 x 108) = 1.33
Ques 11: If the refractive index of glass is 1.5 and that of water is 1.33, then :
1. What will be the refractive index of glass with respect to water?
2. What will be the refractive index of water with respect to glass? (2marks)
Ans: Refractive index of glass = µglass = 1.5
Refractive index of water = µwater = 1.33
So, Refractive index of glass with respect to water = waterµglass = µglass / µwater = 1.5 / 1.33 = 1.127
Refractive index of water with respect to glass = glassµwater = µwater / µglass = 1.33 / 1.5 = 0.89
Ques 12: Explain the application of the refractive index in the construction of lenses. (2 marks)
Ans: When a ray of light moves from one medium to another, its refractive index determines how much it changes direction. This characteristic enables the creation of lenses that can focus light to generate real images, such as those used in film projectors.
Ques 13: Why is the speed of light faster in water than in glass? ( µwater =1.3, µglass= 1.5) (2 marks)
Ans: Water has a refractive index of 1.3, while glass has a refractive index of 1.5. We know that the refractive index of a medium is inversely proportional to the velocity of light in that medium because of the equation, n = c/v. As a result, light travels faster through the water.
Ques 14. What is the refractive index of water? (1 mark)
Ans. The refractive index of water is 1.333.
Ques 15. Why is the refractive index important? (2 marks)
Ans. The higher the refractive index, the slower the light will travel, which causes an increased change in the direction of the light within a material. Lenses with a higher refractive index material can bend more light and allow the profile of the lens to be lower.
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