Ray Optics
1) Reflection 2) Refraction 3) Dispersion
Optics
Optics is that branch of Physics which deals with the study of light energy and phenomena associated with it. It is broadly classified into two categories as shown in the following figure.
Theories of light:-
Corpuscular theory of light-
This theory was proposed by Newton. He suggested that the light propagates rectilinearly as particles called corpuscles. The sensation of different colors is because of the different size of the corpuscles. The energy of light beam is due to the kinetic energy of these corpuscles. Reflection was explained on the basis of repulsion of corpuscles from the
surface and Refraction was explained on the basis of attraction of the corpuscles by the surface. Due to this reason the velocity of the corpuscles should increase on entering any denser medium. This is not found true experimentally and led to the rejection of this theory.
Wave theory of light-
This theory was proposed by Huygens. He suggested that a source of light sends out disturbances in all directions from which the waves spread out in all directions. It was assumed that light travels in the form of longitudinal waves with the velocity 3×108 m/s. Light travel through hypothetical medium called ether having very high elasticity and very low density. The sensation of different colors is because of the different wavelength. Later on in order to explain the phenomenon of polarization the light waves were supposed transverse. This theory failed to explain photoelectric effect of light.
Electromagnetic wave theory of light-
This theory was proposed by Maxwell. He suggested that the light travels as electromagnetic waves with a constant velocity 3×108 m/s. The electromagnetic waves are transverse waves consist of the electric and magnetic field oscillations. This theory can explain reflection, refraction, dispersion, interference, diffraction and polarization etc. but it failed to explain the photoelectric effect of light.
Quantum theory of light-
This theory was proposed by Einstein. He suggested this theory on the basis of Planck’s Quantum theory of Black body radiations. According to this theory, the light is produced, absorbed and propagated as packets of energy called photons. Quantum
theory successfully explains the photoelectric effect, reflection, refraction of light but fails to explain the other phenomena of light.
Dual theory of light-
According to dual theory light propagates both as particle as well as waves. The wave nature dominates when the light interacts with light and particle nature dominates when light interacts with matter. This theory successfully explains all the phenomena of light.
Optical phenomena explained ( √ ) or not explained ( × ) by different theories of light:-
Theory and year of proposing:-
Ray optics
Ray optics is based on the fact that light travels in a straight line. The straight line indicating the path of the light is called a ray and the arrow shows the direction.
A group of rays originating from a point from the source of light is called a beam of light. A beam of light is of different type.
Reflection of light:When light falls on the surface of separation of two media, a part of it returns into the same medium and the remaining part of it is absorbed by the surface. If the surface is polished like a plain mirror, then a large fraction of incident light is sent back into the same medium along a definite direction, this phenomenon is called Reflection.
MirrorMirror is a device which reflects the entire light incident on it. It is mainly of two types 1) Plane Mirror 2) Spherical Mirror- (a) Concave mirror (b) Convex mirror
Reflection of light from a plain mirror-
Laws of Reflection:-
(1) The Incident ray ( IO ), the Reflected ray ( OR ) and the normal ( NO ) at the point of incidence ( O ), all lie in the same plain. (2) The angle of reflection ( i ) and the angle of incidence ( r ) are equal.
Image:-
When rays starting from a point of object suffer a change in direction due to reflection (or refraction) the reflected rays meet or appear to meet at another point, that point is called the image point of that object.
Real image:-
Light rays after reflection or refraction actually meet at a point a real image is formed. A real image can be obtained on the screen. A real image is always inverted.
Virtual image:Light rays after reflection or refraction do not actually meet at a point, but when produced backward, the image is formed at that point is virtual, so a virtual image can not be obtained on the screen. A virtual image is always erect.
Formation of image by plain mirror:-
Nature of image formed by a plain mirror:1) Distance of object in front of the mirror = Distance of object behind the mirror 2) Size of the object = Size of the mirror Thus magnification = 1 3) Image is virtual, laterally inverted and erect; it can not be obtained on the screen 4) The radius of curvature of plain mirror is infinity. Its focal length is therefore Infinity.
Reflection of light from Spherical mirror:-
A reflecting surface which is of the form of a sphere ( hollow ) in which inner or outer surface is reflecting is known as Spherical mirror.
Concave mirror:-
If the outer surface is silvered and reflection takes place from inner surface, the mirror is called concave mirror.
P – Pole is the center of curved surface MM’ of mirror C – It is the center of the sphere from which mirror is formed R – It is the radius of the sphere from which mirror is formed Or R = distance between pole P and center of curvature C. Principal axis – It is the line joining P and C F – Focus is the point at which incident rays parallel to principal axis after reflection from the mirror actually meet. Focal length =F= PC = distance between pole P and focus F F = R/2 Focal plain – Plain passing through focus and normal to the principal axis.
Convex mirror:If the inner surface is silvered and reflection takes place from outer surface, the mirror is called convex mirror.
P – Pole is the center of curved surface MM’ of mirror C – It is the center of the sphere from which mirror is formed R – It is the radius of the sphere from which mirror is formed Or R = distance between pole P and center of curvature C. Principal axis – It is the line joining P and C F – Focus is the point at which incident rays parallel to principal axis after reflection from the mirror appear to meet. Focal length =F= PC = distance between pole P and focus F F = R/2 Focal plain – Plain passing through focus and normal to the principal axis.
Image formed by Concave Mirror:-
Here u = Distance of object v = Distance of image f = Focal length
Image formed by convex mirror:-
Sign Conventions:-
The set of rules to use + or – sign value while doing any problem in optics is called sign Conventions. They are as follows:-
(1) The object is placed on the left side of the mirror, so that the incident rays move from left to right. (2) All measurements are taken from the pole of the mirror. (3) The distance measured in the direction of incident rays are taken as positive + and opposite directions are taken as negative. (4) All measurements of heights above the principal axis are taken as +ve and below the principal axis are taken as –ve.
Mirror formula:1/f = 1/v + 1/u Where f = focal length v = distance of image u = distance of object
Magnification formula:Magnification = m = size of image (hi) / size of object (ho) m = hi/ho = -v/u
Refraction
Deviation or change in the path of light when it travels from one medium to another is known as Refraction.
Note:- Refraction will take place only when light incident in an oblique way ( not normally). If light incident on the surface normally the angle of refraction
will be zero.
When light moves from a rarer medium to denser medium, it bends towards the normal. When light moves from a denser medium to rarer medium, it bends away from the normal.
Laws of refraction:(1) The incident ray, the normal and the refracted ray all lie in a same plain. (2) The ratio of sine of angle of incidence to the sine of angle of refraction is a constant i.e. sin i / sin r = constant = 1n2 Refractive index of one medium (1) with respect to another medium (2) = 1n2 This law is also known as Snell’s law of Refraction.
Relative Refractive Index of two MediaLet PQRS be the path of a ray of light passing successively through air, water, glass And it is emerging in the air again.
For the refraction at point Q, at air-water interface nwa = sin i ------- (1) sin r1 Again, at water-glass interface, ray of light refracted at point R, so ngw = sin r1 -------(2) sin r2 Finally, ray of light again refracted at point S on glass-air interface. nag = sin r2 ------- (3) sin e Multiplying equation (1), (2), (3) we get nwa×ngw×nag = sin i × sin r1 × sin r2 sinr1 sin r2 = sin i sin e But ےi = ےe sin e
Therefore
sin i = 1 sin e
Hence nwa×ngw×nag = 1 ngw = 1 nwa×nag But according to principle of reversibility nga×nag = 1 or nga = 1/nag
ngw = nga/nwa or nwg = nwa/nga Therefore, refractive index of water with respect to glass is equal to the ratio of the absolute refractive index of water to the refractive index of glass.
Apparent Position of an objectDue to refraction depth of a tank cannot be known. The apparent depth of the tank is given by 1/n times the original depth.
n = (real or original depth / apparent depth)
If R is real object position then A is apparent position. Refraction index of the liquid with respect to air is n = OR OA
Lens:Lens is a transparent portion covered by two spherical or one spherical and one plane surface. The lenses are shown below :
Image formed by convex lens:-
Here u = Distance of object v = Distance of image
f = Focal length
Image formed by Concave lens:-
Position of object
Position of image
Nature of image Virtual, erect and diminished
Ray diagram
(i) At infinity
At focus
2F
F
O
F
2F
u is -ve v and f are +ve B
B'
(ii) At any other position
Between C and F
Virtual, erect and diminished
O F 2F u,v and f all are -ve
A
F A'
Sign Conventions:-
The set of rules to use + or – sign value while doing any problem in optics is called sign conventions. They are as follows:(1) The object is placed on the left side of the lens, so that the incident rays move from left to right. (2) All measurements are taken from the pole of the lens. (3) The distance measured in the direction of incident rays are taken as positive + and opposite directions are taken as negative. (4) All measurements of heights above the principal axis are taken as +ve and below the principal axis are taken as –ve.
Lens formula:1/f = 1/v - 1/u
Where f = focal length v = distance of image u = distance of object
Magnification formula:Magnification = m = size of image (hi) / size of object (ho)
m = hi/ho = -v/u
Magnification of inverted images is taken as –ve and for erect image, it is taken as +ve.
Power of lens
The ability of a lens to converge or diverge is called power (P) of the lens. It is defined as the reciprocal of the focal length P = 1/f. The S.I. unit of power of a lens is Dioptre.
Dispersion
The splitting of white light into its constituent colours is called dispersion. The colour sequence is given by the acronym V I B G Y O R- violet, indigo, blue, and green, yellow, orange and red. This colour pattern is called a spectrum.
Dispersion occurs because refraction or bending of light differs with the colour. The speed of light of light of different colours in a medium like glass, water etc. is different.It has been observed that the refractive index of glass for violet colour is more than that for violet colour is more than that for red colour. The speed of light, however is same for all colour in free space or vaccum.
White light screen R O Y G B I V
Dispersion of light