Introduction: Light

Light is a form of energy that enables us to see things. Light starts from a source and bounces off objects which are perceived by our eyes and our brain processes this signal, which eventually enables us to see.

Nature of Light

Light behaves as a:

• ray, e.g. reflection

• wave, e.g. interference and diffraction

• particle, e.g. photoelectric effect

Laws of Reflection

• The angle of incidence is equal to angle of reflection

• Incident ray, reflected ray and normal all lie in the same plane.

Light incident on another medium

When light travels from one medium to another medium it either:

• gets absorbed (absorption)

• bounces back (reflection)

• passes through or bends (refraction)

Characteristics of light

• Speed of light c=λ×μ, where λ is its wavelength and μ is its frequency.

• Speed of light is a constant which is 2.998×10⁸m/s or approximately 3.0×10⁸m/s.

Reflection of light by other media-

A medium that is polished well without any irregularities on its surface will cause regular reflection of light. For example, a plane mirror. But even then some light gets absorbed by the surface.

Fermat’s Theorem-

The principle of least time: Light always takes the quickest path between any two points (which may not be the shortest path).

Plane mirror-

Any flat and polished surface that has almost no irregularities on its surface that reflect light is called as a plane mirror.

Characteristics of images

Images can be real or virtual, erect or inverted, magnified or diminished. A real image is formed by the actual convergence of light rays. A virtual image is the apparent convergence of diverging light rays.

If an image formed is upside down then it is called inverted or else it is an erect image. If the image formed is bigger than the object, then it is called magnified. If the image formed is smaller than the object, then it is diminished.

Image formation by a plane mirror

• The image formed by a plane mirror is always virtual and erect.

• Object and image are equidistant from the mirror.

Principle of Reversibility of light

If the direction of a ray of light is reversed due to reflection off a surface, then it will retrace its path.

Spherical mirror

Consider a hollow sphere with a very smooth and polished inside surface and an outer surface with a coating of mercury so that no light can come out. Then if we cut a thin slice out of the shell, we get a curved mirror, which is called a spherical mirror.

Relationship between focus and radius of curvature-

Focal length is half the distance between pole and radius of curvature.

F = R/2

Curved Mirror

A mirror (or any polished, reflective surface) with a curvature is known as a curved mirror.

Important terms related to spherical mirror:

• Pole (P): The midpoint of a spherical mirror.

• Centre of curvature (C): The centre of the sphere that the spherical mirror was a part of.

• The radius of curvature (r): The distance between the centre of curvature and the spherical mirror. This radius will intersect the mirror at the pole (P).

• Principal Axis: The line passing through the pole and the centre of curvature is the main or principal axis.

• Concave Mirror: A spherical mirror with the reflecting surface that bulges inwards.

• Convex Mirror: A spherical mirror with the reflecting surface that bulges outwards.

• Focus (F): Take a concave mirror. All rays parallel to the principal axis converge at a point between the pole and the centre of curvature. This point is called as the focal point or focus.

• Focal length: Distance between pole and focus.

Rules of ray diagram for representation of images formed

We draw the ray diagram to locate the image of an object formed. The intersection point of at least two reflected will give the position of image of the point object. The two rays that can be used to draw the ray diagram are:

• A ray parallel to the principal axis should pass through the focus after reflection in case of concave mirror, or appear to diverge in case of convex mirror.

• A ray passing through the focus of the concave mirror or directed towards the focus in case of convex mirror, should appear parallel to the principal axis after reflection.

• A ray which is passing through the centre of curvature in a concave mirror or directed in case of convex mirror, should reflect along the same path.

• A ray when incident obliquely to principal axis on a concave or convex mirror is also reflected obliquely.

Image formed by convex mirror

Sign convention for ray diagram-

Distances measured towards positive x and y axes (coordinate system) are positive and towards negative x and y-axes are negative. Keep in mind the origin is the pole (P). Usually, the height of the object is taken as positive as it is above the principal axis and height of the image is taken as negative as it is below the principal axis.

Mirror formula and Magnification

• 1/v + 1/u = 1/f where ‘u’ is object distance, ‘v’ is the image distance and ‘f’ is the focal length of spherical mirror, which is found by similarity of triangles.

• The magnification produced by a spherical mirror is the ratio of the height of the image to the height of the object. It is usually represented as ‘m’.

Position and Size of image formed-

Size of image can be found using the magnification formula m = h’/h = – (v/u) If m is -ve it is a real image and if it is +ve it is a virtual image.

Refraction of light-

Bending of the light rays as it passes from one medium to another medium is known as refraction of light.

Absolute and Relative Refractive Index-

Refractive index of one medium with respect to another medium is called relative refractive index. When taken with respect to vacuum, it’s known as an absolute refractive index.

Refraction through a rectangular glass slab-

When the light is incident on a rectangular glass slab, it emerges out parallel to the incident ray and is laterally displaced. It moves from rarer to denser medium and then again to the rarer medium

Refractive Index-

• The extent to which light bends when moving from one medium to another is called refractive index. This depends on the ratio of the speeds in the two media. The greater the ratio, more the bending.

• It is also the ratio of the sine of the angle of incidence and the sine of the angle of refraction, which is a constant for any given pair of media. It is denoted by:
• n = sin∠i/sin∠r = speed of light in medium 1/speed of light in medium2

Refraction at curved surfaces:

When light is incident on a curved surface and passes through, the laws of refraction still hold true. For example lenses.

Spherical lenses

They are the lenses formed by binding two spherical transparent surfaces together. Spherical lenses formed by binding two spherical surfaces bulging outward are known as convex lenses while the spherical lenses formed by binding two spherical surfaces such that they are curved inward are known as concave lenses.

Important terms related to spherical lenses

• Pole (P): The midpoint or the symmetric centre of a spherical lens is known as its Optical Centre. It is also called as the pole.

• Principal Axis: The line passing through the optical centre and the centre of curvature.

• Paraxial Ray: A ray close to principal axis and also parallel to it.

• Centre of curvature (C): The centres of the spheres that the spherical lens was a part of. A spherical lens has two centres of curvatures.

• Focus (F): It is the point on the axis of a lens to which parallel rays of light converge or from which they appear to diverge after refraction.

• Focal length: Distance between optical centre and focus.

• Concave lens: Diverging lens

• Convex lens: Converging lens

Image formation in Lenses using Ray Diagrams

• Rules for drawing the ray diagrams are as follows-

1. A ray of light which is parallel to the principal axis will pass through the principal focus after refraction from the convex lens.

2. A ray of light passing through principal focus, will emerge parallel to principal axis after refraction from the convex lens.

3. A light ray passing through optical centre will emerge out without any deviation.

Image formed by the Convex Lens for various positions of the object

Image formed by the Convex Lens for various positions of the object

Lens formula and magnification-

Lens formula: 1/v = 1/u = 1/f, gives the relationship between the object-distance (u), image-distance (v), and the focal length (f) of a spherical lens.

Power of a Lens-

The degree of convergence or divergence of light rays is expressed in terms of power. So, the reciprocal of focal length is known as its power. It is represented by letter P. The power is given by-

P = 1/f

The SI unit of power is dioptre. It is represented by D. Power of concave lens is negative and power of convex lens is positive.

Dispersion of White Light by Glass Prism-

When light falls on the prism it splits the incident light into band of colours. The sequence of colours observed are VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange and Red). This band of colour is known as Spectrum.

This splitting of incident light into different colours is known as Dispersion. This splitting is due to bending of light rays at different angles. Violet light bends most whereas red light bends least. The phenomenon of rainbow is also due to dispersion of light.

Total Internal Reflection-

When a light passes from denser to rarer medium and angle of incidence is greater than critical angle, the light will reflect in the denser medium.

Condition for Total Internal Reflection-

• Light should pass from denser to rarer medium

• Angle of incidence should be greater than the critical angle.

Critical angle –

it is defined as angle of incidence for which angle of refraction is 90 degrees.

Atmospheric Refraction-

• Twinkling of Stars-
  
  When star light enters the atmosphere, it undergoes refraction. Due to this refractive index changes as the light bends towards the normal. The apparent position of the stars appears slightly different from the actual position. Since the physical conditions of the earth’s atmosphere are not stationary, the apparent positions of stars keep on changing. That is why they appear to twinkle.

• Advance Sunlight and Delayed Sunset-
  
  The sun is visible 2 minutes before the actual sunrise or sunset appears 2 minutes after the actual sunset has taken place is due to atmospheric refraction.

Sky appears blue in color-

• The colour of the sky appears blue due to scattering of light. When the sunlight passes through the atmosphere, fine particles in air will scatter the blue colour more strongly than red.

Sky appears red in color during sunrise and sunset-

• During sunrise and sunset, light from the Sun near the horizon passes through thicker layers of air and larger distance in the earth’s atmosphere before reaching our eyes. Light from the Sun overhead would travel relatively shorter distance, resulting in white appearance of sun. Near the horizon, most of the blue light and shorter wavelengths are scattered away by the particles. Therefore, the light that reaches our eyes is of longer wavelengths, hence the reddish appearance.