This document provides an overview of optics and concepts related to reflection and refraction of light, including: - Dispersion of light occurs due to the refractive index and wavelength of light. Total internal reflection occurs when light travels from an optically dense medium to a less dense one at an angle greater than the critical angle. - Reflection and refraction follow specific laws when light interacts with plane and curved surfaces. Multiple images can form when light reflects between two mirrors. - Refractive index is the ratio of light speeds in different media and determines how much light bends when passing from one medium to another. Optical fibers use total internal reflection to transmit light signals with low loss.

1. Std : 11th Year : 2020-21
Subject : PHYSICS
CHAPTER 9 : OPTICS
MAHARASHTRA STATE BOARD

2. CAN YOU RECALL?
• What are laws of reflection and refraction?
• What is dispersion of light?
Dispersion of light is the splitting of white light into its
constituent colors due to the refractive index of the
surface and the wavelength of the light.
• What is refractive index?
The ratio of the velocity of light in a vacuum to its
velocity in a specified medium.

3. CAN YOU RECALL?
• What is total internal reflection?
Total internal reflection is the phenomenon of
bouncing back of light in the same medium
after striking the boundary of a rarer medium.
• How does light refract at a curved surface?
When the ray falls on any. point it makes
some angle with normal and following law
of reflection the reflected ray make equal
angle with normal as incident ray goes
backward.
• How does a rainbow form?
When sunlight hits a rain droplet, some of
the light is reflected. The electromagnetic
spectrum is made of light with many different
wavelengths, and each is reflected at a
different angle.

4. 9.1 Introduction
• “See it to believe it” is a popular
saying.
• In order to see, we need light.
• What exactly is light and how are
we able to see anything?
• We know that acoustics is the term
used for science of sound.
• Similarly, optics is the term used for
science of light.
• There is a difference in the nature of
sound waves and light waves.

5. 9.4 REFLECTION
9.4.1 Reflection from a plane surface:
a) If the object is in front of a plane reflecting surface, the image is virtual and
laterally inverted.
b) If we are standing on the bank of a still water body and look for our image
formed by water, the image is laterally reversed, of the same size and on the
other side.
c) If an object is kept between two plane mirrors inclined at an angle 𝜃 (like in a
kaleidoscope), a number of images are formed due to multiple reflections from
both the mirrors.

6. 9.4 REFLECTION
9.4.1 Reflection from a plane surface
𝑛 =
360
𝜃
Let N be the number of images seen.
I. If n is an even integer, 𝑁 = (𝑛 − 1),
irrespective of where the object is.
II. If n is an odd integer and object is
exactly on the angle bisector, 𝑁 =
𝑛 − 1 .
III. If n is an odd integer and object is
off the angle bisector, 𝑁 = 𝑛
IV. If 𝑛 is not an integer, 𝑁 = 𝑚, where
𝑚 is integral part of 𝑛.

7. • Find number of images formed according to given case
(a) 8, 9 (b) 9, 8
(c) 8, 8 (d) 9, 9
Ans: The number of images formed in two
plane mirrors inclined at an angle A to
each other is given by the below formula.
Number of images n = 360/A – 1
The number of images formed
n = (360/A)-1, if (360/A) is even integer.
If (360/A) is odd integer, the number of images formed n = (360/A)-1 when the object is kept
symmetrically, and n = (360/A) when object is kept asymmetrically.
If (360/A) is a fraction, the number of images formed is equal to its integral part.
As the angle gets smaller (down to 0 degrees when the mirrors are facing each other and
parallel) the smaller the angle the greater the number of images.
Here, the angle A between the mirrors is 40 degrees.
Case (a): The object is symmetrically placed.
The number of images formed = (360/40)-1, we get 8 images.
Case (b): The object is asymmetrically placed.
The number of images formed = (360/40), we get 9 images.
Hence, the number of images formed are 8 and 9 respectively.

8. Example: A small object is kept symmetrically between two plane mirrors
inclined at 380. This angle is now gradually increased to 410, the
object being symmetrical all the time. Determine the number of
images visible during the process.
Solution: According to the convention used in the table above,
𝜃 = 380
∴ 𝑛 =
360
38
= 9.47
∴ 𝑁 = 9
This is valid till the angle is 400 as the object is kept symmetrically
Beyond 400, n > 9 and it decreases upto
360
41
= 8.78.
Hence now onwards there will be 8 images till 410.

9. If a ray of light comes to an interface between
two media and enters into another medium of
different refractive index, it changes itself
suitable to that medium. This phenomenon is
defined as refraction of light.
Absolute refractive index:
Absolute refractive index of a medium is the
ratio of speed of light in vacuum to that in the
given medium.
𝑛 =
𝑐
𝑣
Medium having greater value of n is called
optically denser.
Relative refractive index:
9.5 Refraction

10. Do you know ?
(a) Logic behind the convention 2
1
𝑛: Letter n is the
symbol for refractive index, 𝑛2 corresponds to
refractive index of medium 2 and 2
1
𝑛 indicates that it
is with respect to medium 1. In this case, light
travels from medium 1 to 2 so we need to discuss
medium 2 in context to medium 1.
(b) Dictionary meaning of the word refract is to change
the path. However, in context of Physics, we should
be more specific. We use the word deviate for
changing the path. During refraction at normal
incidence, there is no change in path. Thus, there is
refraction but no deviation. Deviation is associated
with refraction only during oblique incidence.
Deviation or changing the path or bending is
associated with many phenomena such as
reflection, diffraction, scattering, gravitational
bending due to a massive object, etc.

11. Illustrations of refraction:
1) 𝑛𝑤𝑎𝑡𝑒𝑟 ≅
𝑅𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ
𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ
tan 𝑟 =
𝑥
𝐴
≅ sin(𝑟) and
tan 𝑖 =
𝑥
𝑅
≅ sin(𝑖)
∴ 𝑛 =
sin(𝑟)
sin(𝑖)
=
𝑥
𝐴
𝑥
𝑅
=
𝑅
𝐴
∴ 𝑛 =
𝑅𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ
2) A stick or pencil kept obliquely in a
glass containing water appears
broken as its part in water appears
to be raised.
9.5 Refraction
Fig.: Real and apparent depth.

12. Small angle approximation:
For small angles, expressed in radian,
sin 𝜃 ≅ 𝜃 ≅ tan 𝜃
For example, for
𝜃 = 300 =
𝜋
6
𝑐
= 0.5236𝑐,
We have sin 𝜃 = 0.5
In this case the error is 0.5236 − 0.5 = 0.0236
in 0.5, which is 4.72 %.
For practical purposes we consider angles less
than 100
where the error in using sin 𝜃 ≅ 𝜃 is
less than 0.51 %. (Even for 600, it is still 15.7
%) It is left to you to verify that this is almost
equally valid for tan 𝜃 till 200 only.
9.5 Refraction

13. Example: A crane flying 6 m above a still, clear water lake sees a fish underwater.
For the crane, the fish appears to be 6 cm below the water surface.
How much deep should the crane immerse its beak to pick that fish?
For the fish, how much above the water surface does the crane
appear? Refractive index of water 4/3.
Solution: For crane, apparent depth of the fish is 6 cm and real depth is to be
determined.
For fish, real depth (height, in this case) of the crane is 6 m and
apparent depth (height) is to be determined.
𝑛 =
𝑅
𝐴
=
𝑅𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ
For crane, it is water with respect to air as real depth is in water and
approve depth is as seen from air ∴ 𝑛 =
4
3
=
𝑅
𝐴
=
𝑅
6
𝑅 = 8 𝑐𝑚
For fish, it is air with respect to water as the real height is in air and
seen from water. ∴ 𝑛 =
3
4
=
𝑅
𝐴
=
6
𝐴
𝐴 = 8 𝑚

14. • For angles of incidence greater than 𝑖𝑐, the angle of refraction become larger
than 900
and the ray does not enter into rarer medium at all but is reflected
totally into the denser medium. This is called total internal reflection.
• During total internal reflection TIR, it is total reflection and no refraction.
• The corresponding angle of incidence in the denser medium is greater than or
equal to the critical angle.
9.6 Total internal reflection
Fig.: Total internal reflection.
• Critical angle for a pair of refracting media
can be defined as that angle of incidence in
the denser medium for which the angle of
refraction in the rarer medium is 900.
sin 𝑖𝑐 =
1
𝜇
𝜇 sin 𝑖𝑐 = 1 sin 900
• For commonly used glasses of
𝜇 = 1.5, 𝑖𝑐 = 41049′ ≅ 420 𝑎𝑛𝑑 𝑓𝑜𝑟 𝑤𝑎𝑡𝑒𝑟 𝑜𝑓
𝜇 =
4
3
, 𝑖𝑐 = 48035′ (𝐵𝑜𝑡ℎ, 𝑤𝑖𝑡ℎ 𝑟𝑒𝑠𝑝𝑒𝑐𝑡 𝑡𝑜 𝑎𝑖𝑟)

15. Do you know ?
In Physics the word critical is used when
certain phenomena are not applicable or
more than one phenomenon are
applicable.
Some examples are as follows.
i. In case of total internal reflection, the
phenomenon of reversibility of light is
not applicable at critical angle and
refraction is possible only for angles of
incidence in the denser medium
smaller than the critical angle.
ii. At the critical temperature, a
substance coexists into all the three
states; solid, liquid and gas.
iii. For liquids, streamline flow is possible
till critical velocity is achieved.

16. 9.6 Total internal reflection
9.6.1 Applications of total internal reflection:
I. Optical fibre:
• An optical fibre essentially consists of an
extremely thin (slightly thicker than a human
hair), transparent, flexible core surrounded by
optically rarer (smaller refractive index),
flexible cover called cladding.
• Entire thickness of the fibre is less than half a
mm. (Fig.(a)).
• An optical signal (ray) entering the core
suffers multiple total internal reflections
(Fig.(b)) & emerges after several kilometers
with extremely low loss travelling with highest
possible speed in that material (~ 2,00,000
km/s for glass).
Fig. (a): Optical fibre construction.
Fig. (b): Optical fibre working.

17. 9.6 Total internal reflection
9.6.1 Applications of total internal reflection:
Some of the advantages of optic fibre communication are listed below.
a) Broad bandwidth (frequency range)
b) Immune to EM interference
c) Low attenuation loss
d) Electrical insulator
e) Theft prevention
f) Security of information
Fig. (a): Optical fibre construction. Fig. (b): Optical fibre working.