CHAPTER 13
LIGHT
13.0 Introduction
Light is that form of energy which
makes object visible to our eye. The branch of physics which deals with the
nature of light, its sources, properties, effects and vision is called optics. For the sake of convenience optics
is divided into two parts namely geometrical optics and physical optics.
Geometrical optics treats propagation
of light in terms of rays and is valid only if wavelength of light is much
lesser than the size of obstacles. It concerns with the image formation and
deals with the study of simple facts such as rectilinear propagation, laws of
reflection and refraction by geometrical methods.
13.1 Reflection and Refraction
When a light ray traveling in a medium encounters a boundary
leading into a second medium, part of all the incident ray is reflected back in
to the first medium.
13.1.1
Object and Image
A point source of light is an object (real) in general. Although
we can imagine of an vertical point object which is clear from the ray diagrams
drawn below.
A point is called image where
light ray intersect or the point from which light rays appear to originate
after reflection
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From
geometry p = q and h = h’
Let
us define lateral magnification 
for plane mirror M = 1.
13.1.2 Rotation of mirror
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Let f be angle of incidence in first
position of mirror M1 M2. Further, let mirror is
rotated through angle q, then
normal will also rotate by same angle is same sense.
d1 = Deviation in first position of mirror = p –
2f
d2 = Deviation in second position of mirror = p –
2 (q
+ f) \ d1 – d2 = p – 2f – {p – 2(q +
f)}
= 2q |
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Thus, the angle turned by the reflected
ray is twice the angle turned by the mirror.
13.1.3 Velocity of image
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x0 ® X
co-ordinate of object xM ® X co-ordinate of
mirror. xI ® X co-ordinate of
image. |
Consider an object (O) standing in
front of a plane mirror. Then image is formed behind mirror, such that
\ u = v xM – x0 = xI
– xM
\ Velocity
of image VI = 
=
\ VIx = 2Vmy – V0x
So, this is the relation among
velocities of image, mirror and object respectively.
Note that velocities towards right
are taken positive and towards left are taken negative.
However, if the object starts
moving parallel to mirror, they
yI = y0
Ţ 
Ţ VI = V0
Velocity of image with respect to observer is then calculated
using basic equation of relative motion,
= velocity of A w.r.t. B = 
13.1.4 Deviation
(a) Single reflection: The deviation suffered by incident
ray due to reflection is given by
Particular case I:
When i = 0 (normal incidence)
dmax = p
Particular case II: When i ® 
(Grazing incidence)
(b) Multiple reflection: In this case net deviation suffered by
incident ray is algebraic sum of deviation due to individual reflection.
dnet = Sdi
Where di = Deviation due to
single reflection
13.2 Reflection by Spherical mirrors
(i) A spherical mirror is a part of a
spherical reflecting surface. When the reflection takes place from the inner
surface and outer surface is polished or silvered, the mirror is known as concave mirror. When the reflection
takes place from the outer surface and the inner surface is polished or
silvered, the mirror is known as convex
mirror.
(ii) The centre
of curvature of a mirror is the centre of the spherical surface of which
the mirror is a part.
(iii) The radius
of curvature R is the radius of
spherical surface of which the mirror is a part.
(iv) The pole of the mirror is the centre of the
mirror point.
(v) The principal
axis is the line joining the centre of curvature C with the pole P of the
mirror.
(vi) The aperture
is the diameter of the mirror.
(vii) The principal
focus is the point on the principal axis, through which a ray of light
parallel to the principal axis, after reflection, passes (in case of concave
mirror) or appears to pass (in case of concave mirror).
(viii) Focal
length is the distance between the pole P
and the principal focus F. It is
represented by f (distance PF in figure). For a spherical mirror of small aperture, the focal length is half of
the radius of curvature (f = R/2).
(ix) The law of reflection is valid for
reflections from spherical mirrors i.e.
angle of incidence I = angle of
reflection r.
(x) Mirror formula: For all spherical mirrors.
where u = distance of the object from the pole
of
mirror, v = distance of the image from the pole
of
mirror, f = focal length of the mirror and R = radius of curvature the mirror.
13.2.1 Sign convention
(i) All the distances
along the principal axis (i.e., u, v and f) are measured with respect to pole of a mirror.
(ii) Measured in the
direction of light ray are taken as positive and those measured opposite to the
direction of light ray as negative.
(iii) The distances
(heights) measured above the principal axis are taken as positive while distances
below the principal axis are taken as negative
(iv) According to this
sign convention, the focal length and radius of curvature of a concave mirror are negative, while
those of convex mirror are positive.
(v) If the object is
situated on left hand side (as it is so normally), the object distance u is always
negative.
13.2.2 Real and virtual images
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Real
image |
Virtual
image |
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(a) When the rays of light after reflection
from the mirror actually meet the image, then the image formed is said to be
real. |
(a) When the rays of light after reflection
do not meet (i.e., they diverge)
and appear to be diverging from the image, then the image is said to be
virtual. |
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(b) A real image can be obtained on a screen. |
(b) A virtual image cannot be obtained on
the screen. |
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(c) For an erect object, the real image
formed after reflection is always inverted. The size may be less than, equal
to or greater than the actual size of the object. |
(c) For an erect object, the virtual image
is always erect. The size of the virtual image may be less than, equal to or
greater than the size of the object. |
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(d) For a convex mirror, for any position of
the object, the image is virtual. |
13.2.3 Magnification due to a mirror
(i) Transverse or linear magnification m is defined as
(ii) It can be proved that for both the
concave and convex mirrors:
or 
or 
13.3 Refraction of light
Refractive index (µ) of a medium
depends upon speed of light in the medium.
Greater the refractive index of a
medium lesser will be the speed of light in the medium.
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Snell’s law. When a light rays falls on the boundary of two transparent
media, the light ray may or may nor deviate from its original path according
to law. q1 angle of incidence q2 angle of refraction |
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µ1 = refraction index
of first medium w.r.t. vaccume
µ2 = refractive index
of second medium w.r.t vaccume
From diagram q1 > q2
Ţ sinq1 > sin q2
Ţ µ1
< µ2 [from
Snell’s law]
Medium
of refractive index µ1 is said to be optically rarer medium in which
light ray moves faster in comparison to the optically denser medium having
refractive index µ2.
13.3.1 Apparent shift
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When an object is placed in one
medium and viewed from other medium the image seen by the observer and the
object lie at different positions. |
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Note:
When object is in
denser medium image shifts towards boundary, away from the boundary otherwise.
Shift in image 
13.4 Total
internal reflection
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A light ray in denser medium
falls on the boundary between denser and rarer medium, it deviates away from
the normal. The angle of incidence in the denser medium for which angle of
refraction in rarer medium is 90°, is defined as critical angle for the given
two media. |
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From Snell’s law
Critical
angle 
13.5
Refraction from a Spherical Surface
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Consider
two transparent media having indices of refraction µ1 and µ2, where the boundary between the two
media is a spherical surface of radius R. We assume that µ1 < µ2. A single ray leaving from object,
point O and focusing at image, point I. |
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Formula
for spherical surface:
The
lateral magnification m is the ratio of the image height to the object height (
).
Magnification: 
13.6
Thin Lenses
A lens is an optical system with
two refracting surfaces. The simplest lens has two spherical surfaces close
enough together that we can neglect the distance between them (the thickness of
the lens). We call this a thin lens.
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Lenses are of two basic types convex
which are thicker in the middle than at the edges and concave for which the
reverse holds.
13.6.1
Focus
Unlike a mirror, a lens has two
foci.
First focus (F1): It is defined as a point at which
if an object (real in case of a convex lens and virtual for concave) is placed,
the image of this object is formed at infinity.
Second focus or principal focus (F2): A narrow beam of light travelling
parallel to the principal axis either converge (in case of a convex lens) or
diverge (in case of a concave lens) at a point F2 after refraction from the
lens.
13.6.2
Lens maker’s formula and lens formula
Consider an object O placed at a
distance u from a convex lens as shown in figure. Let its image I after two
refractions from spherical surfaces of radii R1 (positive) and R2 (negative) be formed at a distance v from the
lens. Let v1 be the distance of image formed by refraction
from the refracting surface of radius R1. The formula is given by following formula:
If the refractive index of the
material of the lens is µ and it is placed in air, µ2 = µ and µ1 = 1 so that eq. (iv) becomes
This is called the lens maker’s
formula because it can be used to determine the values of R1 and R2 that are needed for a given refractive index
and a desired focal length f.
Lens
formula:
13.7
Prism
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A prism has two plane surfaces
inclined to each other. The angle between the surfaces is called angle of
prism. It can be noted that the angle of deviation suffered by light at the
first surface AB is not cancelled
out by the deviation at the second surface AC, but it is added to it. Hence the net deviation of emergent
light with respect to the incident light is d. |
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From the figure it can be observed
that
i1 = x + r1 and
i2 = y + r2
on adding the equation we get
i1 + i2 = x + y + r1 + r2 …
(i)
Also
it may be noted that
d = x + y and A
= r1 + r2
on adding the equations, we get
A + d
= x + y + r1 + r2 … (ii)
Hence from equation (i) and (ii) we
can conclude that
i1 + i2 = A + d
13.7.1
Angle of minimum deviation
As d = i1 + i2
– A hence for d to be minimum 
should be zero.
\ 
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hence 
di2 = – di1 on integrating we get
i2 = – i1, hence for minimum deviation it is necessary that
magnitude of i1 and i2 should be same. In such a
situation angle r1 and r2 will also become equal.
Since
A = r1 + r2
= 2r1
\ r1 = A/2
from d = i1 + i2 – A at the
time of minimum deviation i1
= i2 in magnitude hence
dm
= 2i1 – A
or 
Using snells’s law
we get 
13.7.2 Deviation by a prism of small
angle
If angle of prism A is small, r1 and r2
(as r1 + r2 = A) and hence i1
and i2 will also be small.
Since for small angles in sin q = q. The deviation is given by:
d = (µ – 1) A
13.7.3 Condition of No emergence
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The light will not emerge out of
a prism for all values of angle of incidence if at face AB for i1 = max
= 90°, at face AC: r2 > qC This condition solves to µ > cosec (A/2) |
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13.8 Dispersion of Light
When white light passes through a
prism it splits up into constituent colours. This phenomenon is called dispersion and arises due to the fact
that refractive index of a prism is different for different wavelengths.
…
(1)
But as for a prism, 
… (2)
From expressions (1) and (2) it is
clear that dispersive power like refractive index has no units and dimensions
and depends on the material of the prism.
13.8.1 Dispersion without deviation
As angle of deviation depends upon
the prism material, we are in a position to put together prisms of different
materials in such a way that the net outcome is such that while dispersion
remains, deviations get cancelled out.
This can be done when deviation (d1) produced by first prism is equal
and opposite to the deviation (d2)
produced by the second prism.
So, for net resultant deviation,
13.8.2 Deviation without dispersion
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If d1 and d2 are the deviation the deviation
suffered by the mean light ray in 1st and 2nd prism,
then the following is the condition to get deviation without dispersion.
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where w1 and w2 are the respective dispersive
powers.
13.9 Optical Instrument
13.9.1 Simple Microscope
A simple convex lens is said to be
a simple microscope when the object is placed between focus and optical centre
of law and the eye of the observer is kept close to the lens. The image found
in this case will be erect and enlarged.
Magnifying
power [Angular magnification]: For an optical instrument it is defined as the ratio of angle
made by image at the eye to the maximum angle made by the object at the eye
when placed at least distance of distinct vision (i.e. 25 cm denoted by D)
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(a) |
(b) |
Figure (a) shows an object of height h placed at distance D from the eye of the observer. Let a is
the angle made by the object at the eye. Hence 
Figure (b) shows the simple microscope
where the image of height h’ is
making an angle b at the optical centre of lens (or eye of the observer) hence 
Therefore 
13.9.2 Compound Microscope
A compound microscope is primarily used for higher magnification.
A compound microscope consists of two convex lens, objective lens (of small
focal length f0 and of
small aperture) and an eyepiece (a convex lens of moderate focal length(f e)), and bigger aperture.
L = Length of tube.
13.9.3 Telescope
Telescope is an optical instrument
to clearly observe the distant object.
Astronomical
telescope
This telescope is used to observe
heavenly objects like moon, distant stars and planets etc. The image formed by
this telescope is virtual and inverted. Since the heavenly bodies are almost
round, so the inverted images do not affect the observations.
Terrestrial
telescope
If in the astronomical telescope, a
lens of short focal length f is
placed at 2f from intermediate image
(figure), it will erect the intermediate image at a distance 2f on the other side of it and this image
will act as an object for eye lens. So now the final image will be erect with
respect to object. This lens is called erecting
lens and as for it m = –1, the MP
and length of telescope for relaxed eye will be
MP =
L = f0
+ fe + 4f
This is telescope is called terrestrial telescope and is used to
see distant terrestrial objects such as a cliff or a tree.
