Light Reflection and Refraction

• Light is a form of electromagnetic radiation that causes the sensation of sight. In vacuum/air light travels with a constant speed of 3 X 10 ^8 m/s. Ordinarily light travels in straight lines but truely speaking light exhibits wave character. Wavelengths of visible light vary form about 400 nm for violet light to about 700 nm for red light.

• The straight line path along which a light wave travels, is called a ray of light. A bundle of rays is called beam of light.

• When light falls on a surface separating two media, a part of light is reflected, a part is refracted and a part is absorbed.

• A highly polished surface mostly reflects the light falling on it.

• A transparent medium e.g., glass, water etc., refracts most of the light falling on it.

• When a number of rays, starting from a point after reflection or refraction, meet or appear to meet at another point, the second point is called the image of the first point.

• The image formed is real if the reflected or refracted rays actually meet at a point. The image is virtual if the rays do not actually meet, but appear to meet at a point when produced backwards.

• A real image can be obtained on the screen but a virtual image cannot be obtained on the screen.

• Two basic laws of reflection of light are :

(a) The angles of incidence (i) is equal to the angle of reflection (r).

(b) The incidence ray, the reflected ray and the normal lie on the same plane.

• Image of an extended object formed object formed by a plane mirror has the following characteristics :

(i) The image formed is virtual and erect.

(ii) The image is of same size as the object.

(iii) The image is formed as far behind the mirror as the object is in front of it.

(iv) The image is laterally inverted.

• If the reflecting surface of a mirror is curved one. it is called a curved mirror. Most commonly used curved mirror is the spherical mirror. A spherical mirror is that whose reflecting surface is spherical.

• A spherical mirror whose reflecting surface is curved inwards is called concave mirror. A spherical mirror whose reflecting surface is curved outwards is called a convex mirror. The centre of the reflecting surface of a mirror is called its pole (P).

• The centre of the sphere, the given mirror forms a part of which, is called the centre of curvature (C) of the spherical mirror. Centre of curvature of a mirror lies outside its reflecting surface. For a concave mirror the centre of curvature lies in front of it but for a convex mirror it lies behind the mirror.

• The distance from pole to centre of curvature is known as the radius of curvature of given mirror. Thus, R = PC.

• A straight line passing through the pole and the centre of curvature of a spherical mirror is called its principal axis. Principal focus of a spherical mirror is a point on its principal axis where light rays coming parallel to its principal axis, after reflection, actually converge or appear to diverge. Distance from pole to principal focus is called focal length (f) of given mirror.

• Focal length of a spherical mirror is half of its radius of curvature. Thus, f = R/2 or R = 2f.

• The position of the image formed by a spherical mirror can be found by considering any two of the following rays :

(i) The ray incident parallel to the principal axis, after reflection, passes through the principal focus of a concave mirror or appears to pass through the principal focus of a convex mirror.

(ii) A ray passing through the principal focus of a concave mirror or a ray directed towards the principal focus of a convex mirror is reflected parallel to the principal axis of mirror.

(iii) A ray passing through the centre of curvature in a concave mirror or a ray directed towards the centre of curvature in a convex mirror, after reflection, retraces its path.

(iv) A ray incident obliquely to the principal axis at the pole point is reflected obliquely so that angles subtended by the two rays from principal axis are equal and in mutually opposite directions.

 • A convex mirror always forms a virtual, erect and diminished image of a real object. When an object is placed at infinity, the point sized image is formed behind the mirror at its principal focus. However, for any other position of the object the diminished image is formed behind the mirror between pole P and principal focus F.

• While considering reflection from spherical mirrors, we follow the New Cartesian Sign Convection. According to this convection :

 (i) The object is taken on the left of the mirror, i.e., the incident ray strikes the mirror from left hand side.

(ii) All the distances parallel to the principal axis are measured from the pole of the mirror.

(iii) Distances in the direction of the incident light are taken positive and in the opposite direction negative. In other words, distances right to the pole are taken positive and distances left to the pole negative.

(iv) The heights measured upwards are taken positive and the heights measured downwards are taken negative.

• Mirror formula is a relation between the object distance (u), the image-distance (v) and the focal length (f) of the mirror. According to mirror formula.

1/u + 1/v = 1/f    or    1/u + 1/v = 2/R

The mirror formula is true for concave and convex mirrors bot, irrespective of the fact whether the image formed is real or virtual. However, proper sign for u, v, f and R be applied as per sign convention followed.

• Magnification (m) of a spherical mirror is defined as the ration of the height of the image to the height of the object.

Magnification (m) = Height of the image (h’)/Height of the object (h) = – v/u

Magnification for real and inverted image is negative. Magnification for a virtual and errect image is positive.

• Concave mirrors are used in torches, search lights and head lights of the vehicles to obtain a powerful parallel light beam. Large concave mirrors are used to concentrate sunlight in solar furnaces. Concave mirrors are used as shaving mirror. Dentists use concave mirrors to see large image of the teeth of patients.

• Convex mirrors are used in vehicles near the driver seat to have a view of traffic coming from behind. As convex mirrors form erect and diminished images only, they enable the driver to view much larger area than would be possible with a plane mirror.

• Whenever a light ray undergoes oblique refraction form one transparent medium to another, the ray changes its path. it is on account of change in speed of light on entering the second media.

• Two basic laws of refraction of light are :

(i) The incident ray, the refracted ray and the normal to the separation surface at the point of incidence, all lie in the same plane.

(ii) The ration of sine of the angle of incidence (i) to the sine of angle of refraction (r) is a constant. It is known as Snell’s law. Thus, according to Snell’s law 

sin i / sin r = constant = n21

 Here, n21 is known as the refractive index of the second medium with respect to the first medium.

• When a light ray is refracted from medium number 1 into medium number 2, the refractive index of medium 2 w.r.t medium 1 (n21) is given by :

n21 = Speed of light in medium 1 v1)/Speed of light in medium 2 (v2)

• Similarly, the refractive index of medium 1 with respect to medium 2 is given by :

n12 = Speed of light in medium 2 (v2)/Speed of light in medium 1 (v1)

• Absolute refractive index n of a given medium is defined as :

n = Speed of light in vacuum or air (c)/ Speed of light in given medium (v)

• Refractive index is a unitless term. Moreover, absolute refractive index of a medium has a value equal to one or greater than one.

• It is found that 

n21 = v1/v2 = n2/n1

• For a given wavelength and pair of media, n21 is a constant whose value depends only upon the optical properties of the two media and is independent of the angle of incidence.

• A medium with larger refractive index is called optically denser medium and the medium with lesser refractive index is called optically rarer medium.

• A ray of light travelling from a rarer medium to a denser medium bends towards the normal. However, a ray of light travelling from a denser to a rarer medium bends away from the normal.

• Refractive index of air is generally taken as 1. Refractive index of water w.r.t air is 1.33 and that of crown glass w.r.t. air is 1.52. Refractive index of diamond is maximum equal to 2.42.

• Whenever a light ray suffers refraction through a glass slab of constant width, the emergent ray is parallel to the incident ray along the original direction. However, the emergent ray suffers a finite lateral displacement.

• A lens is a part of a transparent material either bound by two spherical surfaces or bound by one plane and the other spherical surface. A lens is convex if it is thick in the middle and thin at edges. On the other hand, a concave lens is thin in the middle and thick at edges.

• A convex lens converges the incident light beam and is, thus, known as a converging (or convergent) lens. A concave lens diverges the incident light beam and is known as a diverging lens.

• As a lens has two surfaces, each surfaces has its own centre of curvature. A straight line passing through the two centres of curvature of a lens is called its principal axis.

• The optical centre of a lens is the point on its principal axis, a ray of light passing through which goes undeviated.

• The effective diameter of the circular outline of a spherical lens is called its “aperture”. For a thin lens aperture of lens is generally much less than its radius of curvature.

• The principal focus of a lens is the point on its principal axis where a beam of light coming parallel to its principal axis actually converges to or appears to diverge from after refraction from the lens. A lens has two principal foci F1 and F2, one on each side of the lens.

• The position of the image formed by a lens can be found by consideration any two of the following rays :

(i) A ray incident parallel to the principal axis, after refraction, passes through the principal focus on other side of lens in a convex lens or appears to diverge from the principal focus located on the same side of a concave lens.

(ii) A ray of light passing through the principal focus in a convex lens or appearing to meet at the principal focus in a concave lens emerges parallel to the principal axis after refraction.

(iii) A ray of light passing thorough the optical centre of lens emerges without suffering any deviation after refraction.

• For a real object a concave lens always forms a virtual, errect and diminished image. For an object situated at infinity the point sized image is formed at the principal focus F1. In all other cases the diminished image is formed on the same side of the lens, as the object, between optical centre O and principal focus F1.

• In dealing with lenses we use the same Cartesian sign convention as followed for mirror except that now all the distances are measured from the optical centre of the lens.

• Lens formula is a relations correlating u, v and f for a lens. According to lens formula, we have : 1/v – 1/u = 1/f

The relation is true for all lenses and all types of images formed. However, appropriate sign convention must be followed for u, v and f.

• The magnification (m) produced by a lens is given by 

m  = Height of the image (h’)/ Height of the object (h) = v/u

Magnification of a lens is -ve for a real and inverted image but +ve for a virtual and errect image.

• The power (P) of a lens is defined as the reciprocal of its focal length (f).

 P = 1/f

• SI unit of power is dioptre (D), where 1 D = 1 m^-1. The power of a convex lens is positive and that of a concave lens is negative.

• If a number of thin lenses having powers P 1, P 2, P 3 … are placed in contact then the net power (P) of the lens combination is equal to the algebraic sum of the individual powers .

P = P 1 + P 2 + P 3 + ….