Ray Optics

 

 

Light is an electromagnetic wave (wavelength:- about 400 nm to 750 nm) that travels in a straight line in a vacuum with a very fast speed, c = 2.99792458 × 10⁸ ms^–1 (approximately  3 × 10⁸ ms^–1).

The straight line in which light travels is called a Light Ray, and a bundle of rays is called a beam of light.

Optics :-

The branch of physics in which the nature and the properties of light are studied is called optics.

There are two branches of optics:-

(1) Ray Optics or Geometrical Optics

(2) Wave Optics or Physical Optics

(1) Ray optics is that part of optics which studies the motion of light by considering it as a ‘ray’. According to the assumption of ray optics, as long as light travels in a homogeneous medium, its path is a straight line. Where two mediums meet, the light rays are bent.

The diffraction and interference of light cannot be explained under geometrical optics because the results are pure by geometrical optics as long as the size of the objects is much larger than the wavelength of the light.

(2) Wave optics is that branch of optics which studies phenomena like interference, diffraction, polarization, etc., for which geometrical optics does not give correct results. It tells the wave form of light.

Reflection of Light :-

When a ray of light enters from one medium to another, it strikes the reflecting surface and returns back to the same medium. This phenomenon is called reflection of light.

In the reflection of light, the speed, frequency and wavelength of light remain unchanged, but the intensity decreases (since some part of the light is absorbed by the reflecting surface during reflection).

 

Laws of Reflection :-

1. Incident ray, reflected ray, normal all three lie in the same plane.

2. Both the angle of incidence (i) and the angle of reflection (r) are equal.

Mirror :-

The structure formed by polishing one side of a transparent material is called a mirror.

Or

A mirror is a reflective surface that light does not pass through, but bounces off of and this produces an image.

Types of Mirrors :-

There are mainly three types of mirrors:-

1. Plain Mirror
2. Spherical Mirror :- (1) Convex Mirror (2) Concave Mirror
3. Parabolic Mirror

 

Mirror terminology :-

(1) Pole/vertex (P) :- Pole is the mid point of a spherical mirror.

(2) Center of curvature (C) :- The center of curvature is the center of the sphere of which the spherical mirror is a part.

(3) Principal Axis:- The principal axis is an imaginary line passing through the pole and center of curvature of the spherical mirror.

(4) Principal focus:- The principal focus is a point on the principal axis where a ray of light, parallel to the principal axis, after reflection, actually meets (concave mirror) or appears to meet (convex mirror).

(5) Focal Length:- The focal length is the linear distance between the pole and the principal focus.

(6) Radius of curvature :- Radius of curvature is the linear distance between pole and center of curvature.

(7) Aperture :- The diameter of the reflecting surface of a spherical mirror is called its aperture (aa’ and bb’ in the figure).

(8) Focal Plane:- The plane passing through the focus and perpendicular to the principal axis is called focal plane.

(9) Paraxial Rays: – These rays make a small angle with the normal at the point of incidence and are therefore close to the principal axis.

(10) Marginal rays: – The angle of incidence of these rays is large.

Cartesian sign convention for mirrors :-

 

 

To get the formula for reflection by spherical mirrors and refraction by spherical lenses, we have to follow a sign convention.

We will use the Cartesian sign convention, according to which all distances are measured from the pole of the mirror or the optical center of the lens.

According to the New Cartesian Sign Convention:-

1. The distances measured upwards (perpendicular to the principal axis) are taken as positive.
2. Distances measured downward (perpendicular to the principal axis) are taken as negative.
3. The distances measured in the direction of the incident rays are taken as positive &
4. The distances measured in the opposite direction of the incident rays are taken as negative.

Note: – The focal length and radius of curvature of a concave mirror are negative, the focal length and radius of curvature of a convex mirror are positive and the focal length and radius of curvature of a plane mirror is infinite.

 

Laws of image formation from mirror :-

The image is formed at the point where any two of the following four rays meet or appear to meet after reflection from the mirror. When the rays actually meet, a real image is formed which is always inverted and if the rays only seem to meet, then a virtual (imaginary) image is formed which is always upright.

(1) Incident ray parallel to principal axis :-

A ray of light which is incident parallel to the principal axis passes through the focus (concave mirror) or appears to pass (convex mirror) after reflection from the mirror.

(2) The ray passing through the focus :-

A ray of light which passes through the focus (concave mirror) or directed towards the focus (convex), becomes parallel to the principal axis after reflection from the mirror.

(3) Ray passing through the center of curvature :-

A ray of light which passes through the center of curvature (concave mirror) or appears to pass (convex mirror), after reflection from the mirror, returns back following the path of incidence.

(4) Ray incident at pole :-

A ray of light which is incident at the pole of the mirror, after reflection from the mirror, returns in the opposite direction at the same angle (with the principal axis).

 

Next Topic :-

Image Formation By Mirrors

1. Image formation by concave mirror
2. Image formation by convex mirror
3. Image formation by plane mirror