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'.

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 $2 \times 10^8 \text{ ms}^{-1}$.

Question 223 marksShort AnswerSection B

$3 \times 10^8 \text{ ms}^{-1}$

Light — Reflection and Refraction

Refractive Index

Official answer

n_{xz}

Refractive index

Speed of light

9/8

1.125

2 x 10^8 m/s

Marking scheme

1. $Write the relation between relative refractive indices and absolute refractive indices. (0.5 marks)$
2. $\frac{9}{8}$
3. $n_{xy} = v_y / v_x$
4. $2 \times 10^8 \text{ ms}^{-1}$

Hint

$n_{ab} = n_a / n_b = v_b / v_a$

Quick oral answer

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

Common mistakes

1. $n_{xy} = v_x / v_y$
2. $n_{xy}$

Analysis and explanation

n_{xy} = n_x / n_y = v_y / v_x

Interesting facts

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

Question details

Q22 of 30 questions

Board: CBSE
Class: Class 10
Subject: Science
Year: 2020
Section: Section B
Marks: 3
Type: Short Answer
Chapter: Light — Reflection and Refraction
Topic: $Refractive Index$
Bloom's level: Applying
Syllabus topic: $Refraction of light; Refractive index; Speed of light in different media.$

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Frequently asked questions

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

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

$Which chapter does this question come from in Science?$

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

$What topic does this question cover in Science?$

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

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

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