 # HC Verma Solutions Class 11 Chapter 21 Speed of Light

HC Verma Solutions Class 11 Chapter 21 Speed of Light provides a thorough and contemporary approach to understand questions related to light and the time taken to reach a certain point. In order to help students understand the concepts clearly, we are offering free HC Verma solutions for class 11 physics students. The solutions are for important chapter problems that will help students understand the light’s speed in a better way. The solutions are carefully prepared by experts to meet the needs of the students and help them have a better learning experience. However, in chapter 21 students will mainly come across problems such as:

• Finding the angular velocity when the speed of light, refractive index, distance is given.
• Problems on finding the speed of light as per Foucault experiment, where the distances between fixed, rotating mirror, source and lens are given along with angular speed.
• Students will solve questions based on the Michelson experiment where values of distance, refractive index are given.

The HC Verma solutions bring in a fresh approach to understanding class 11 physics topics and questions that students need to practice and understand before attempting exams especially competitive ones like JEE.

Students can further explore topics like;

1. Historical Introduction
2. Fizeau Method
3. Foucault Method
4. Michelson Method

## What Is The Speed Of Light?

The speed of light is universally taken as a constant which is 300,000 km/s. It is referred to the maximum speed of the light and is denoted by ‘c’.

## Class 11 Important Questions In Chapter 21

1. While conducting the Fizeau method, the light is said to have traveled up to 8.6 km and then returned. What will happen if the distance is measured at 8.6 m? What challenges can be faced?

2. In the Michelson method while measuring the speed of light, can you state the advantage of using a polygonal mirror with a larger number of faces?

3. When will the speeds of yellow and red light be exactly the same?

(a) in a vacuum (b) in the air (c) both in vacuum and air (d) none of these.

4. Name the method or methods that can be used to measure the speed of light in a laboratory?

(a) Michelson method (b) Foucault method (c) Fizeau method (d) Roemer method

5. We pass light through a closed cylindrical tube containing gas. Now we slowly pump out the gas. What will happen to the speed of light inside the tube?

(a) It will increase (b) It will decrease (c) It remains constant (d) The speed will first increase and then gradually decrease.

## HC Verma Solutions Vol 1 Speed of Light Chapter 21

Question 1: In an experiment to measure the speed of light by Fizeau’s apparatus, following data are used:

Distance between the mirrors = 12.0 km,

Number of teeth in the wheel = 180.

Find the minimum angular speed of the wheel for which the image is not seen.

Solution:

In the Fizeau’s apparatus,

Distance between the mirrors, D = 12.0 km = 12×103 m

Number of teeth in the wheel, n = 180

Speed of light = 3×108 ms-1

we know,

Speed of light, c = (2Dnω)/π

=> ω = cπ/(2Dn) rad/sec = cπ/(2Dn) x 180/π degree/sec

=> ω = [3×108]/[24×103] = 1.25 x 104 degree/sec

Question 2: In experiment with Foucault’s apparatus, the various distances used are as follows:

Distance between the rotating and the fixed mirror = 16 m

Distance between the lens and the rotating mirror = 6 m,

Distance between the source and the lens = 2 m.

Solution:

Distance between fixed and rotating mirror = R = 16m

Distance between lens and rotating mirror = b = 6m

Distance between source and lens = a = 2m

Angular speed = ω = 356 rev/s = 356 × 2π rad/sec

Shift in image = s = 0.7 cm = 0.7 x 10-3 m/s

Now,

Speed of light = c = $\frac{4R^2ωa}{s(R+b)}$

= $\frac{4 \times 16^2 \times 356 \times 2π \times 2}{0.7 \times 10^{-3} \times (16+6)}$

= 2.975 x 108 m/s

Question 3: In a Michelson experiment for measuring speed of light, the distance travelled by light between two reflections from the rotating mirror is 4.8 km. The rotating mirror has a shape of a regular octagon. At what minimum angular speed of the mirror (other than zero) the image is formed at the position where a non rotating mirror forms it?

Solution:

Distance travelled by the light wave between two reflections from the rotating mirror = D = 4.8 km = 4.8 × 103

Number of faces of the mirror = N = 8

In the Michelson experiment, the speed of light = c = (DωN)/2π

Where, ω is angular speed of the mirror.

Or ω = (2πc)/DN rad/s = c/(DN) rev/sec

= [3×108]/[4.8×103x8]

= 7.8 x 103 rev/sec