Chapter 7: Geometrical and Physical Optics

Physical optics deals with the wave nature of light whereas geometric optics deals with the particle nature of light.

Electromagnetic waves

Electromagnetic waves

Electromagnetic waves are a type of wave that consists of oscillating electric and magnetic fields that travel through space at the speed of light. They are produced by the acceleration of charged particles and include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Electromagnetic waves have a wide range of applications, including communication, medical imaging, and energy production.

Electromagnetic Spectrum

It can be categorized by its frequency. The full range of waves is called the electromagnetic spectrum.

Interference

The phenomenon of superimposition of two or more waves having the same frequency emitted by two coherent sources.

Diffraction

It is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of the geometrical shadow of the obstacle/aperture.

Single-Slit Experiment

A diffraction pattern will also form on the screen if the barrier contains only one slit.

Young’s Double Slit Experiment

The incident light on a barrier that contains two narrow slits, separated by distance d. On the right there is a screen whose distance from barrier L, is much greater than d.

Constructive and Destructive Interference

constructive interference: d sinθ = m λ

destructive interference: d sinθ = (m+1/2) λ

where,

• m = 0, 1, 2, 3, etc.

• λ = wavelength of light

• d = distance

Angle of incidence

The angle that the incident beam makes with the normal is called the angle of incidence.

Angle of reflection

The angle that the reflection makes with the normal is called the angle of reflection.

Angle of refraction

The angle that the transmitted beam makes with the normal is called the angle of refraction.

Laws of reflection

The incident, reflection, and transmitted beams of light all lie in the same plane.The relationship between the incident and reflected ray:angle of incidence = angle of reflection

Maximum index of refraction

n = c/v

• c = speed of light (3*10^8 m/s)

• v = speed of light in a particular medium

• n = refractive index

Snell’s Law

n 1 sin θ′1 = n2 sin θ′2

• If n2>n1, the beam will bend/refract toward the normal.

• If n2<n1, the beam will bend away from the normal.

• Here, n1 and n2 are the refractive indexes in respective mediums.

Total internal reflection

Total internal reflection occurs when:

n1> n2 and θ1> θc,

where, θc = sin−1 (n2/n1)

• θc is the critical angle.

• n1 and n2 are the refractive indexes in respective mediums.

Mirror

A mirror is an optical device that forms an image by reflecting light.

Plane mirror

• Our image is behind the mirror and stands at an equal distance as we stand before the mirror.

• An image is said to be real if light rays actually focus on the image. A real image can be projected onto the screen.

• The images produced by the flat mirror are virtual.

• In a flat mirror, we see an upright image because it's virtual.

• In real images, the image is upside down.

• The image formed by plane mirrors is neither diminished nor enlarged.

Spherical mirror

A spherical mirror is a mirror that’s curved in such a way that its surface forms part of a sphere.

Relationship between focal length and center of curvature

F = R/2

where,

• F = focal length (the focal length of an optical system is a measure of how strongly the system converges or diverges light).

• R = radius of curvature (the radius of curvature is the radius of a hollow sphere of which the mirror/spherical mirror is a part).

Concave mirror

A mirror whose reflective side is caved in toward the center of curvature.

Convex mirror

A mirror whose reflective side curving away from the center of curvature.

Mirror equation

1/so + 1/si =1/ f

• so = object distance

• si = image distance

• f = focal length

Magnification equation

M = hi/ho = -si/so

• M = magnification

• hi = height of the image

• ho = height of the object

• si = image distance

• so = object distance

conclusion on mirrors

Converging lens

Bi-convex lens

Diverging lens

Bi-concave lens

Power of Lens

P = 1/f

• P = power of the lens

• f = focal length of lens

light

• Light is a form of energy that travels in a straight line when in one medium (material).

• The speed of light is 3x108m/9c m/s (or 300,000,000 m/s)

Visible Spectrum

The continues of colors that make up with light.

Geometric optics

Using light rays to determine how light behaves when it strikes an object.

light ray

is a line and arrow representing the direction and straight-line path of light.

Real Image

An image which light actually comes from the image

Virtual image

an image which light does not arrive at or actually come from the image location, light only appears to come from the image

Centre of curvature

The centre of the sphere whose surface was used to make an image

Principal axis

This is a line through the centre of curvature which runs through midpoint of mirror.

Focus

• Focus is the point at which lights rays parallel to principal axis converge when reflected.