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# Fundamentals of Physics Chapter 35 Solutions: Interference

Halliday Resnick and Walker Fundamentals of Physics Volume 2 Solutions for Chapter 35 ‘Interference’ is designed for those who will appear in Class 12 board exams along with several competitive examinations. These solutions help you acquire the foundational concepts associated with Interference that will help you in the exams. In this chapter of Resnick Halliday, you will learn about several topics like the light as a wave, Young’s slit experiment, interference, and double slit intensity, interference from the thin lens, Michelson’s interferometer, etc.

Resnick Halliday & Walker Physics Volume 2 Interference Solutions include 105 problems. All the questions of the chapter are divided into two sections named Modules and Additional problems. The questions are based on the JEE Mains and JEE Advanced exam pattern and also contain basic questions. By solving them, you will understand each and everything about coherent sources, interference patterns, central maxima, fringe width, constructive and destructive Interference, etc. The solutions listed here will support you in understanding the concepts incorporated with this chapter.

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## Important Topics of Halliday Resnick and Walker Fundamentals of Physics Volume 2 Solutions Chapter 35: Interference

This chapter is listed with some beautiful concepts that you are going to learn. Let’s familiar to them-

Coherent Sources- When to call two sources are said to be coherent? See here, the sources are said to be coherent if the light waves possess the same frequency and the constant phase difference.

We have a laser that’s one of the common examples of coherent sources.

You will need coherent sources for doing practical of Interference in your college lab, as the Interference phenomenon can only be observed, having coherent sources as a primary light source.

Huygen’s Principle- Before heading towards the assumptions that Huygen gave in his principle,  just have a little overview of wavefronts.

What are wavefronts?

It is a set of points or you can say, a surface at which the generating wave possesses the same phase difference. And, it moves in a forward direction with a speed of light. Wavefronts can be of three types-

➢     Cylindrical wavefront.

➢     Planar wavefront.

➢     Spherical Wavefront.

So, you must have understood about wavefronts. Now, See what Huygen’s told us in his principle-

➢     He told every wave is moving with the wavefronts and every point on the wavefronts could be considered as a source of secondary wavelets

➢     Whatever the new wavefront generated will be tangential to the surface of all secondary wavelets.

Fringe width- It is nothing, the distance between the constructive dark and bright fringes, and denoted by an abbreviation ‘β’.

If we talk about what’s the fringe width in the case of constructive interference. So, you must know that the fringe width is constant and to be known as a linear fringe width.

Central Maxima- In single-slit diffraction, there are some points at which secondary wavelets reinforce each other which results in the maximum intensity at those points. These points are called points of central maxima.

The Intensity in Two-Slit Interference-

In young- slit Interference, if the two waves having an intensity I0, then the resulting wave Intensity I must be equal to-

I =  4 I0  cos^ 2 φ/2

where φ = [ 2 π / λ ] . Sin θ

Apart from this, we will also learn some other useful chapters like Double-slit- diffraction, Thin Film Interference, Michaelson’s Interferometer in this chapter.

### Exercise Discussion of Halliday Resnick and Walker Fundamentals of Physics Volume 2 Solutions Chapter 35: Interference

Module 1:  Light As a Wave

Module- 35.1 questions will let you understand how light behaves as a wave. It has 13 questions and in which you will be asked to determine the refractive indices, speed of light in different materials like glass and diamonds, etc.

Module 2:  Young’s Interference Experiment

Module-35.2 has questions based on the assumptions of Young’s Interference experiment. You will be able to solve questions on the Double-Slit experiment after having a proper practice of questions that are included in this Module. You will practice 15 questions.

Module 3: Interference And Double-Slit Intensity

Module-35.3 will judge your knowledge on Interference and Double-Intensity. It has 6 questions. In questions, you will find the amplitude of the resulting wave, the ratio of intensity at some point P to the intensity at the centre of the pattern, etc. Also some questions on phaser method as well. You need to determine the rate at which phasors rotates around the origin, and the angle between the phasors, etc.

Module 4: Interference From Thin Films

Module-35.4 has 44 questions in total, and are based on the concept of Interference from Thin films. In these, you will be asked to find the thickness of films, the angles between the slides, the Intensity of resulting waves, etc.

Module 5: Michelson’s Interferometer

In Module-35.5, there are 4 questions based on Michelson’s Interferometer. In questions of this module, you will be asked to answer the wavelength of fringe pattern, index of refraction of air, and also the thickness of films, etc.