1. Light is
that form of energy which causes sensation of sight of your eyes. In fact,
light is a part of electromagnetic radiation spectrum having its wavelength
ranging from about 400 nm to 700nm.
2. In vacuum
light of any wavelength (or any frequency) travels with a speed c = $ 2.99792458
\times 10^8 $ m/s but for ordinary calculations this value may be considered as c = $ 3 \times 10^8 $ m/s. The speed of light in vacuum is the highest speed attainable in
nature. Moreover, speed of light in vacuum is independent of the relative
motion between the source and the observer. No physical signal or message can
travel with a speed greater than c.
3. As the
wavelength of light is very small compared to the size of ordinary objects, a
light wave can be considered to travel from one point to another point along a
straight line path. Such a path is called a ray of light of right and a bundle
of rays constitutes a beam of light.
4. In
reflection of light, the light rays return to the same medium after striking
the surface of another medium (say a mirror). The wavelength and the speed of
light remains the same.
5. There are
two basic laws of reflection, which are followed for every short of reflection.
According to these
(i) The
incident ray, reflected ray and the normal at
the point of incidence all lie in the same plane.
(ii) Angle
of incidence (i) = angle of reflection (r).
6. For
reflection from a plane mirror, the image formed is always erect, virtual and
laterally inverted. The image is of exactly the same size as the object and the
image is formed as such behind the mirror as the object is in front of it.
7. For a
spherical mirror in the mid-point of reflecting surface is called its pole. The
line passing through pole and the center of curvature of mirror is called its
principle axis.
8. The principle
focus of a spherical mirror is a point on its principle axis, where a beam of
light incident parallel to principle axis of mirror, after reflection, actually
converges to (in case of a concave mirror) or appears to diverge from (in case
of a convex mirror). Distance of principle focus from pole is called the local
length of given mirror.
9. Focal
length of a spherical mirror is half of its radius of curvature i.e., f = R/2.
10. As per
Cartesian sign convention system for mirrors, the light ray is taken to travel
from left to right. All distances are measured from the pole as origin. The
distance measured in the same direction as the incident light are taken as
positive and those measured in the opposite direction are taken as negative.
Thus, the distances to the right of pole will be + ve but distances to the left
of pole will be – ve. Again distances above the principle axis are taken as +
ve but distances below it – ve.
11. A concave
mirror may form either a real or a virtual image depending upon the position of
the object relative to the mirror. A convex mirror forms only virtual images.
12. If an
object is placed at a distance u from the pole of a mirror of focal length f
and its image is formed at a distance v from the pole, then according to mirror
formula, we have \[\frac{1}{u} + \frac{1}{v}=\frac{1}{f}=\frac{2}{R}\].
13. If a thin
linear object of height h is situated normally on principle axis of mirror at a
distance u and its image of height h’ is formed at a distance v from the pole,
then the linear magnification m is defined as \[M = \frac{h'}{h} = -\frac{v}{u} = \frac{f}{f-u} = \frac{f-v}{f}\]-ve
magnification means inverted image and +ve magnification means erect image.
14. When a
light ray travels obliquely from one transparent medium to another, it changes
the direction of its path at the interface of the two media. This is called
“refraction” of light.
15. There are
two laws of refraction, which are as follows:
(i) The
incident ray, the refracted ray and the normal to the interface at the point of
incidence, all lie in the same plane.
(ii) The
ratio of the sine of the angle of incidence in 1st medium t sine the
angle of refraction in second medium is a constant, knows as the refractive
index of 2nd medium with respect to the 1st medium.
Mathematically, \[\frac{sin (i)}{sin (r)} = n_{21}\]Second law
of refraction is known as Snell’s law.
16. Value of
refractive index depends upon the pair of media and the wavelength of light but
is independent of the angle of incidence.
17. When a
light ray obliquely enters from an optically rarer medium to an optically
denser medium, the light ray bends towards the normal. However, if a light ray
travels from denser to rarer medium, it bends away from the normal.
18. Absolute
refractive index of a transparent medium is defined as the ratio of the speed
of light vacuum (c) to the speed of light in given medium (v) i.e., $ n = \frac{c}{v}$. It can be
show that $ n_{21} = \frac{n_2}{n_1} = \frac{v_1}{ v_2} = \frac{\lambda_1}{\lambda_2}$. It is found
that $n_{12} = \frac{1}{n_{21}} $.
19. When a
light ray passes through a parallel sided slab of a transparent medium, the
final emergent ray is parallel to the incident ray, but is laterally displaced
by a distance d given by \[d = t \frac{sin (i – r)}{cos r}\]The value
of lateral shift depends upon (a) thickness (t) of the transparent slab, (b)
angle of incidence (i) and (c) refractive index of the material of slab.
20. When an
object situated in medium number 2 is viewed from medium number 1, the apparent
depth (height) of object appears to be different from its real depth 9height)
and these are co-related as: \[\frac{d_{Real }}{ d_{Apparent}} = n_{12} = \frac{1}{n_{21}}\]
21. If an
object situated in an optically denser medium is viewed by an observer situated
in optically rarer medium, the apparent height is less than its real height.
However, if an object situated in rarer medium is viewed by an observer
situated in denser medium, then the apparent height is found to be more than
its real height.
22. On account
of atmospheric refraction the Sun is visible about 2 minutes before the actual
sunrise and for 2 minutes even after the actual sunset. Thus, Sun also appear
to be of oval shape at the time of sunrise or sunset on account of atmospheric
refraction.
23. For a pair
of media in contact, circuital angle is the angle of incidence in the denser
medium corresponding to which angle of refraction in the rarer medium is 90
degree. If a light ray is incident on the surface of a rarer medium 2 from a
denser medium 1, then \[Sin(i_c) = n_{21}\]Here $ n_{12}$ is the refractive index of 1st (denser) medium with respect
to the 2nd (rarer) medium.
24. Total
internal reflection is the phenomenon of complete reflection of light back into
the denser medium, when a light ray coming from denser medium is incident on
the surface of a rarer medium.Two
essential conditions for total internal reflection are:
(i) The
light ray should travel in a denser medium towards a rarer medium.
(ii) Angle
of incidence in the denser medium should be greater than the critical angle for
the pair of media in contact.
25. Values of
critical angle of glass-air and water-air interfaces are 41.5 degree and
48.75 degree, respectively.
26. The
brilliance of diamond, action of optical fibres and mirage etc., are the
phenomena based on total internal reflection of light.
27. Prism make
use for total internal reflection phenomenon to bend light by 90 degree or by
180 degree or to invert images without changing their size. Such prism have one
angle 90 degree and the other two angles 45 degree each and are known as totally
reflecting prisms or poroprisms.
28. For
refraction at a single spherical surface, all distances are measured from the
pole of the refracting surface. The distances measured in the direction fo
incidence of light are taken as positive and the distances measured in the
opposite direction are taken as negative. If object is considered to be
situated on left side of pole, then the
sign convention agrees with the cartesian coordinate system. Accordingly, all
distances on left side of pole are taken as negative and on right side of pole
as positive. The height measured above the principle axis are taken as positive
as heights measured downwards are taken as negative.
29. For
refraction at a single spherical surface \[\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2 - n_1}{R}\]Where light
beam is going from medium of refractive index n1 to medium of refractive index
n2. The
relation is true for concave as well as convex spherical surfaces and
irrespective of the fact whether refraction is taking places from rarer medium
to denser medium or vice-versa.
30. According
of lens maker’s formula \[\frac{1}{f}=(n_{21}-1)(\frac{1}{R_1}-\frac{1}{R_2})\]Where $n_{21}$ is the refractive index of lens material w.r.t. the surrounding medium, $R_1$ and $R_2$ are the radii of curvature of two surfaces of lens and f its focal length.
31. For image
formed by a thin lens, we have \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\]All the
above relation are the true for convex as well as concave surfaces/lenses and
for real as well as virtual images.
32. Linear
magnification (m) produced by a lens is defined as the ratio of the linear
(lateral) size of the image to that of the object. Thus, \[m = \frac{h'}{h}=\frac{v}{u}=\frac{f-v}{f}=\frac{f}{f+u}\]For erect
and virtual image, m is positive but for an inverted and real image, m is
negative.
33. Power of
lens is a measure of a degree of convergence or divergence of light incident on
it. Mathematically, the power(p) of a lens is defined as the tangent of the
angle by which it converges/ diverges a beam of light falling at unit distance
from the optical centre. For a thin lens power is found to be the reciprocal of
its focal length (f) i.e., \[P = \frac{1}{f}\]SI unit of
power is dioptre (D).
34. Power of a converging
(convex) lens is taken to be positive but that of a diverging (concave) less is
taken negative.
35. For a
combination of two (or more) thin lenses in contact, the effective focal length
of the combination is given by \[\frac{1}{f} = \frac{1}{f_1}+\frac{1}{f_2}+......\]And in term
of power, we have $ P = P_1 + P_2 + ...... $.
36. For a
combination of two or more lenses, the effective magnification for the
combination is given by \[m = m_1 \times m_2 \times m_3 .......\]
