Maharashtra Board Class 12 Physics Chapter 7 Wave Optics PDF Download

7. Wave Optics

Can you recall?

1. What does the formation of shadows tell you about the propagation of light?

2. What are laws of reflection and refraction?

3. What are electromagnetic waves?

4. What is the range of frequencies of visible light?

5. What is meant by the phase at a point along the path of a wave?

7.1 Introduction:

In earlier standards we have learnt that light travels in a straight line while travelling through a uniform and homogeneous medium. The path of light is called a ray of light. On encountering an interface with another medium, a ray of light gets reflected or refracted, changes its direction and moves along another straight line. The reflection is such that (i) the incident ray, the reflected ray and the normal to the boundary surface at the point of incidence are in the same plane and (ii) the angle of incidence, i.e., the angle between the incident ray and the normal to the reflecting surface, is equal to the angle of reflection, i.e., the angle between the reflected ray and the normal. For refraction of light while travelling from medium 1 to medium 2, the laws are (i) the incident ray, the refracted ray and the normal to the boundary between the two media at the point of incidence are in the same plane and (ii) the angle of incidence i, and the angle of refraction r, are related by \(n_1 \sin i = n_2 \sin r\), where, n₁ and n₂ are the absolute refractive indices of medium 1 and medium 2 respectively.

We have also learnt about the reflection of light produced by spherical mirrors and refraction of light through prisms and curved surfaces of lenses. The position and nature of the image (whether real or virtual) depend on the position of objects and the focal length of the mirror or lens.

7.2 Nature of Light

7.2.1 Corpuscular Nature:

The formation of shadows as well as images by mirrors and lenses has been understood by considering rectilinear motion of light rays. This fact led R. Descartes (1596-1650) to propose a particle nature of light in the year 1636. Newton (1642-1726) developed this concept further and proposed that light is made up of particles, i.e., corpuscles which are hard, elastic and massless. A source of light emits these corpuscles which travel along straight lines in the absence of any external force. When the light corpuscles strike a reflecting surface, they undergo elastic collisions and as a result follow the laws of reflection. During refraction, it is the difference in the attractive force between the corpuscles and the particles of the medium that causes a change in the direction of the corpuscles. A denser medium exerts a larger attractive force on light corpuscles to accelerate them along the normal to the boundary. Thus, Newton's theory predicted that the speed of light in denser medium would be higher than that in a rarer medium. This contradicts the experimental observation. In this theory, light of different colours corresponds to corpuscles of different sizes. Newton performed several experiments in optics and could explain their results based on his theory. The study of optical phenomena under the assumption that it travels in a straight line as a ray is called ray optics or geometrical optics as geometry is used in this study. The laws of reflection and refraction and the formation of images that we studied in earlier standards fall under this category.

Teacher's Note

Light behaves like particles when hitting metal surfaces. This is why mirrors and metals reflect light so well, just like how a ball bounces off a wall.

Exam Trick

Remember: Corpuscle = small particle. Newton thought light was made of tiny hard balls. This helped explain reflection but failed to explain interference and diffraction.

Points to Remember

Newton thought light is made of particles called corpuscles.
Corpuscles are hard, elastic, and massless particles.
This theory explained reflection very well.
It could not explain interference, diffraction, and polarization.
Ray optics is based on this corpuscular theory of light.

7.2.2 Wave Nature:

To circumvent the difficulties in corpuscular theory, it was proposed by the Dutch physicist C. Huygens (1629-1695) in the year 1668, that light is a wave. Huygens assumed light to be a wave caused by vibrations of the particles of the medium. As light could also travel in vacuum, he assumed that a hypothetical medium, called ether is present everywhere including in vacuum. Note that this ether is not the substance (ether gas) that we come across in chemistry. There was however, no evidence to prove its existence and thus, it was difficult to accept the concept. In the nineteenth century, certain new phenomena of light namely, interference, diffraction and polarization were discovered. These could not be explained based on corpuscular theory and needed wave theory for their explanation. Huygens' theory could not only explain the new phenomena but could also explain the laws of reflection and refraction, as well as the formation of images by mirrors and lenses. It was then accepted as the correct theory of light. Wave theory showed that if the speed of light waves in denser medium is smaller than that in rarer medium then light bends towards normal. Thus, wave nature of light could explain all the visual effects exhibited by light. The branch of optics which uses wave nature of light to explain the optical phenomena is called wave optics.

In this chapter we are going to study wave optics and learn how the laws of reflection and refraction can be explained assuming the wave nature of light. We will also learn about the phenomena of interference, diffraction and polarization and their explanation based on wave optics. The reason why geometrical optics works in case of formation of shadows, reflection and refraction is that the wavelength of light is much smaller than the reflecting/refracting surfaces as well as the shadow causing objects that one encounters in laboratory or in day-to-day life.

In XIth Std we have learnt Maxwell's equations which suggested that light is an electromagnetic wave. As all waves known till Maxwell's time needed a medium to propagate, Maxwell invoked the all-pervading hypothetical medium ether. The existence of radio waves and their speed being same as that of visible light, were experimentally verified by H. Hertz later in the nineteenth century. Michelson and Morley performed several experiments to detect ether but obtained negative result. The hypothesized ether was never detected, and its existence and necessity was ruled out by Albert Einstein (1879-1955) when he proposed the special theory of relativity in the year 1905, based on a revolutionary concept of constancy of velocity of light.

Teacher's Note

Huygens said light is a wave like water ripples or sound. His idea explained new properties of light that Newton's particle idea could not explain.

Exam Trick

Remember: Huygens = waves. Wave theory explained interference and diffraction perfectly. Ether was imaginary but the wave idea was correct.

Points to Remember

Huygens proposed light is a wave in a medium called ether.
Wave theory explained interference, diffraction, and polarization.
Wave theory also explained reflection and refraction laws.
Ether does not exist but waves are real.
Einstein proved constancy of light speed in his theory of relativity.

7.2.3 Dual Nature of Light:

In the early twentieth century, it was accepted that light has a dual nature. It can exhibit particle nature as well as wave nature under different situations. Particles of light are called photons. We will learn more about it in Chapter 14.

7.3 Light as a Wave:

Light is an electromagnetic wave. These waves are transverse in nature and consist of tiny oscillating electric and magnetic fields which are perpendicular to each other and to the direction of propagation of the wave. These waves do not require any material medium for propagation and can even travel through vacuum. The speed of light in a material medium (v) depends on the refractive index of the medium (n) which, in turn, depends on permeability and permittivity of the medium. The refractive index is equal to the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v). The refractive index of vacuum is 1 and that of air can be approximated to be 1.

Teacher's Note

Light is made of electric and magnetic fields. These fields are perpendicular to each other, just like how length and width are perpendicular in a rectangle.

Exam Trick

Remember: Light is electromagnetic = electric field + magnetic field. Refractive index n = speed in vacuum / speed in medium. Always greater than 1 for any material.

Points to Remember

Light is an electromagnetic wave with electric and magnetic fields.
Both fields are perpendicular to each other and to direction of propagation.
Light does not need any medium to travel through vacuum.
Refractive index shows how much light slows down in a medium.
Refractive index of vacuum is 1 and of air is approximately 1.

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