The refractive index of a medium 'x' with respect to a medium 'y' is 2/3 and the refractive index of medium 'y' with respect to medium 'z' is 4/3. Find the refractive index of medium 'z' with respect to medium 'x'. If the speed of light in medium 'x' is $3 \times 10^8 \text{ ms}^{-1}$ , calculate the speed of light in medium 'y'.

Light — Reflection and Refraction

Refractive Index

Official Answer

The refractive index of medium 'z' with respect to medium 'x' ( $n_{xz}$ ) is $\frac{9}{8}$ (or $1.125$ ).

The speed of light in medium 'y' ( $v_y$ ) is $2 \times 10^8 \text{ ms}^{-1}$ .

Refractive indexSpeed of light9/81.1252 x 10^8 m/s

Marking Scheme

1Write the relation between relative refractive indices and absolute refractive indices. (0.5 marks)
2Correctly calculate the refractive index of medium 'z' with respect to 'x' as $\frac{9}{8}$ or $1.125$ . (1 mark)
3State the formula relating refractive index to the speed of light ( $n_{xy} = v_y / v_x$ ). (0.5 marks)
4Correctly calculate the speed of light in medium 'y' as $2 \times 10^8 \text{ ms}^{-1}$ . (1 mark)

Hint

Remember that $n_{ab} = n_a / n_b = v_b / v_a$ . Use this relation to link the relative refractive indices and velocities of light in different media.

Quick Oral Answer

The refractive index of medium 1 with respect to medium 2 is the ratio of the speed of light in medium 2 to the speed of light in medium 1. It is a dimensionless quantity.

Analysis & Explanation

The refractive index of a medium with respect to another is inversely proportional to the speed of light in those media. Thus, $n_{xy} = n_x / n_y = v_y / v_x$ . By chain-multiplying relative refractive indices, we can find any relation between three or more media. Here, the speed of light in medium 'y' is calculated directly using the definition of relative refractive index in terms of velocities.

Common Mistakes

1Inverting the ratio of speeds (e.g., writing $n_{xy} = v_x / v_y$ instead of $v_y / v_x$ ).
2Confusing the notation $n_{xy}$ (refractive index of x with respect to y) with $n_{yx}$ .

Interesting Facts

A refractive index of less than 1 for one medium with respect to another simply means light travels faster in the first medium than in the second; absolute refractive indices (with respect to vacuum) are always greater than or equal to 1.

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Frequently Asked Questions

How many marks does this question carry in CBSE Class 10 Science 2020?

This question carries 3 marks in the CBSE Class 10 Science 2020 examination.

Which chapter does this question come from in Science?

This question is from the chapter "Light — Reflection and Refraction" in the CBSE Class 10 Science syllabus.

What topic does this question cover in Science?

This question covers the topic "Refractive Index" from CBSE Class 10 Science.

What type of question is this in the CBSE Class 10 Science 2020 paper?

This is a Short Answer question from Section B in the CBSE Class 10 Science 2020 paper.