What is Relative Refractive Index?

S6-SA3-0160

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Relative refractive index tells us how much the speed of light changes when it goes from one transparent material (medium) to another. It's a ratio that compares the refractive index of the second medium to the refractive index of the first medium. Essentially, it shows how much light 'bends' when it crosses the boundary between two specific materials.

Simple Example

Quick Example

Imagine you are running a race. If you run from a smooth road onto a sandy beach, your speed changes. Relative refractive index is like comparing your running speed on the beach to your speed on the road. If light goes from air (like the road) into water (like the sand), its speed changes, and the relative refractive index tells us by how much.

Worked Example

Step-by-Step

Let's find the relative refractive index when light goes from water to glass.

Step 1: Identify the refractive index of the first medium (water). Refractive index of water (n_water) = 1.33.
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Step 2: Identify the refractive index of the second medium (glass). Refractive index of glass (n_glass) = 1.5.
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Step 3: Remember the formula for relative refractive index: n_21 = n_2 / n_1, where n_21 is the refractive index of medium 2 with respect to medium 1.
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Step 4: Substitute the values into the formula. Here, medium 1 is water and medium 2 is glass. So, n_glass_water = n_glass / n_water.
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Step 5: Calculate: n_glass_water = 1.5 / 1.33.
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Step 6: Perform the division: n_glass_water approximately = 1.127.

Answer: The relative refractive index of glass with respect to water is approximately 1.127.

Why It Matters

Understanding relative refractive index is crucial for designing lenses in cameras and eyeglasses, which is key in fields like Medicine (for eye surgery tools) and AI/ML (for computer vision systems). Engineers use it to create optical fibres for fast internet, and scientists in Space Technology use it to study light from distant stars passing through different atmospheres.

Common Mistakes

MISTAKE: Confusing absolute refractive index with relative refractive index. | CORRECTION: Absolute refractive index compares a medium to vacuum (or air), while relative refractive index compares two different non-vacuum media.

MISTAKE: Mixing up which medium is '1' and which is '2' in the formula (n_2/n_1). | CORRECTION: Always remember the formula is 'refractive index of the second medium divided by the refractive index of the first medium'. Light travels FROM medium 1 TO medium 2.

MISTAKE: Assuming relative refractive index always has a unit. | CORRECTION: Relative refractive index is a ratio of two refractive indices, so it is a dimensionless quantity (it has no unit).

Practice Questions

Try It Yourself

QUESTION: If the refractive index of diamond is 2.42 and that of kerosene is 1.44, what is the relative refractive index of diamond with respect to kerosene? | ANSWER: Approximately 1.68

QUESTION: Light travels from medium A to medium B. If the speed of light in medium A is 3 x 10^8 m/s and in medium B is 2 x 10^8 m/s, what is the relative refractive index of medium B with respect to medium A? (Hint: Remember n = c/v, where c is speed of light in vacuum). | ANSWER: 1.5

QUESTION: The relative refractive index of medium P with respect to medium Q is 0.8. If the refractive index of medium Q is 1.6, what is the absolute refractive index of medium P? | ANSWER: 1.28

MCQ

Quick Quiz

Which of the following statements about relative refractive index is TRUE?

It always has a value greater than 1.

It is the ratio of the refractive index of the first medium to the second medium.

It is a dimensionless quantity.

It is used to measure the bending of light only when it enters a vacuum.

The Correct Answer Is:

Relative refractive index is a ratio of two similar quantities (refractive indices), so it has no units, making it dimensionless. It can be less than 1, and it's the ratio of the second medium's refractive index to the first's, not the other way around. It applies to light entering any medium, not just a vacuum.

Real World Connection

In the Real World

Optical fibres, which bring high-speed internet to our homes and power Jio and Airtel networks, rely heavily on the concept of relative refractive index. These fibres are made of different types of glass or plastic, carefully chosen so light stays trapped inside, allowing data to travel long distances without much loss. This principle is also used in endoscopes for medical imaging.

Key Vocabulary

Key Terms

MEDIUM: A substance through which light can travel, like air, water, or glass. | REFRACTIVE INDEX: A number that describes how much light slows down when it enters a specific medium from a vacuum. | DIMENSIONLESS: A quantity that does not have any units, like metres, seconds, or kilograms. | LIGHT REFRACTION: The bending of light as it passes from one medium to another.

What's Next

What to Learn Next

Great job understanding relative refractive index! Next, you should explore 'Snell's Law'. It uses the relative refractive index to calculate the exact angle at which light bends when it passes from one medium to another, which is super useful for designing optical instruments!