Nature of light | Famous Books for UPSC Exam (Summary & Tests) PDF Download

Introduction

• In the past, light was only understood to have wave properties. However, in the early 20th century, it was discovered that the wave theory of light was often insufficient in explaining the interaction between light and matter. It was observed that light sometimes exhibited particle-like behavior, leading to a state of confusion regarding its true nature. Eventually, a modern quantum theory of light emerged, which reconciled the particle and wave properties of light.
• The rectilinear propagation of light, which refers to its ability to travel in straight lines, can be demonstrated by the formation of shadows with sharp edges. When an opaque obstacle is placed between a source of light and a screen, a shadow of the obstacle is cast on the screen. If light passes through a small hole, the resulting shadow is a completely dark area known as the umbra. When an extended source of light, such as a bulb, is used, the umbra is surrounded by a partially dark region called the penumbra.

Reflection of Light

A mirror, such as a highly polished surface, has the ability to reflect a majority of the light that falls upon it. The process of reflection follows the following laws:

• The angle at which light strikes the mirror surface (angle of incidence) is equal to the angle at which it reflects (angle of reflection).
• The incident ray, the normal (perpendicular line) to the mirror at the point of incidence, and the reflected ray all lie in the same plane.

There are two types of surfaces for the reflection of light:

Plane Mirrors: When light reflects off a plane mirror:

• The image formed is virtual (not physically present) and erect (upright).
• The size of the image is the same as that of the object.
• The image is located the same distance behind the mirror as the object is in front of it.
• The image appears laterally inverted (horizontally reversed).

Spherical Mirrors: These mirrors have a curved surface that can be either convex or concave. The reflecting surface of a spherical mirror is part of a sphere.

• Concave mirrors: The reflecting surface curves inward.
• Convex mirrors: The reflecting surface curves outward.

Important terms associated with mirrors:

• Pole: The center of the reflecting surface of a spherical mirror, represented by the letter P.
• Centre of curvature: The center of the sphere from which the reflecting surface of a spherical mirror is a part. It is represented by the letter C.
• Radius of curvature: The radius of the sphere that the reflecting surface of a spherical mirror forms a part of, represented by the letter R.
• Principal axis: An imaginary straight line passing through the pole and the center of curvature of a spherical mirror. It is normal (perpendicular) to the mirror at its pole.
• Focus: The point where incident rays parallel to the principal axis converge or appear to be coming from (in the case of a concave mirror).
• Focal length: The distance between the focus and the mirror's surface, represented by the letter F.
• Aperture: The circular outline or diameter of the reflecting surface of a spherical mirror.
• Relationship between radius of curvature and focal length: For small-aperture spherical mirrors, the radius of curvature is approximately twice the focal length. The focal point lies midway between the pole and the center of curvature.

Uses of Concave Mirrors

• Torchlights, searchlights, and vehicle headlights: Concave mirrors are employed in these applications to produce powerful parallel beams of light.
• Shaving mirrors: Concave mirrors are utilized as shaving mirrors to provide a magnified image of the face, allowing for easier and more precise shaving.
• Dentistry: Dentists use concave mirrors to obtain enlarged images of patients' teeth, aiding in examinations and treatments.
• Solar furnaces: Large concave mirrors are employed to concentrate sunlight, generating intense heat in solar furnaces for various applications.

Uses of Convex Mirrors

Rear-view mirrors in vehicles: Convex mirrors are commonly used as wing mirrors or side mirrors in vehicles. They allow drivers to observe the traffic behind them, providing a wider field of view and an erect, though diminished, image. This aids in safe driving and monitoring the surroundings.

Refraction of Light

• When a ray of light transitions from one medium to another, it changes its direction at the boundary between the two media. This phenomenon is known as refraction. The following are the laws of refraction:
• The incident ray, the refracted ray, and the normal (a line perpendicular to the interface of the media at the point of incidence) all lie in the same plane.
• Snell's Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for light of a specific color and a given pair of media. This constant is referred to as the refractive index of the second medium with respect to the first.
• If I represents the angle of incidence and r represents the angle of refraction, then:
  (sin I) / (sin r) = constant

The Refractive Index

The degree of change in the direction of light when it transitions from one medium to another is quantified by the refractive index. The value of the refractive index for a specific pair of media is dependent on the speed of light in those media. Let's consider a ray of light traveling from medium 1 to medium 2. Denoting V1 as the speed of light in medium 1 and V2 as the speed of light in medium 2, the refractive index of medium 2 with respect to medium 1 is determined by the ratio of the speed of light in medium 1 to the speed of light in medium 2. This is commonly represented as n21. The equation for this can be expressed as:

If medium 1 is vacuum or air, then the refractive index of medium 2 is measured with respect to vacuum. This is referred to as the absolute refractive index of the medium and is denoted by n2. If c represents the speed of light in air and v represents the speed of light in the medium, the refractive index of the medium (n/m) is given by:

The absolute refractive index of a medium is simply known as its refractive index. When comparing two media, the one with the higher refractive index is considered optically denser than the other. Conversely, the medium with the lower refractive index is considered optically rarer. In a rarer medium, the speed of light is higher, while in a denser medium, light slows down and bends towards the normal as it transitions. Conversely, when light travels from a denser medium to a rarer medium, it speeds up and bends away from the normal.

Effects of Refraction

• The bottom of a tank or pond containing water appears raised when viewed from above.
• When viewing printed matter through a thick glass slab, the letters appear raised.
• A partially immersed pencil in a glass of water appears to be displaced at the air-water interface.
• An object placed in water in a glass appears larger than its actual size when viewed from the sides.
• A coin placed in a bowl becomes visible when water is poured into the bowl.
• Objects seen through a turbulent stream of hot air above a fire or radiator appear to waver or flicker due to refraction between the hot air and surrounding cold air.
• The twinkling of stars is caused by atmospheric refraction of starlight as it enters Earth's atmosphere and undergoes continuous refraction due to the changing refractive index.
• The Sun is visible about 2 minutes before sunrise and after sunset due to atmospheric refraction.

Spherical Lenses and Refraction

A lens is a transparent material bound by two surfaces, one or both of which are spherical. There are two types of spherical lenses:

• Convex lens: Also known as a converging lens, it has two outwardly curved spherical surfaces, with the middle thicker than the edges. A convex lens converges light rays and is represented by a double convex shape.
• Concave lens: Also known as a diverging lens, it has two inwardly curved spherical surfaces, with the edges thicker than the middle. A concave lens diverges light rays and is represented by a double concave shape.

Each spherical surface of a lens is part of a sphere, with the centers of these spheres referred to as the centers of curvature of the lens. The principal axis of a lens is an imaginary straight line passing through the two centers of curvature.