The document covers concepts in wave optics, including the laws of reflection and refraction, the nature of light, and the principles of Huygens and interference. It discusses the Young’s double slit experiment, demonstrating the wave nature of light and the conditions necessary for obtaining a stable interference pattern. Additionally, it describes phenomena such as diffraction and the types associated with light waves.

1. Std : 12th Year : 2022-23
Subject : PHYSICS
Chapter 7 : Wave optics
CLASSXII
MAHARASHTRA STATE BOARD

2. Can yourecall ?
1. What does the formation of shadows tell
you about the propagation of light?
2. What are laws of reflection and
refraction?
3. What are electromagnetic waves?
4. What is the range of frequencies of
visible light?
5. What is meant by the phase at a point
along the path of a wave?

3. Laws of Reflection
https://phet.colorado.edu/en/simulations/filter?subjects=light-and-radiation&type=html&sort=alpha&view=grid

4. Laws of Refraction
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6. NATURE OF LIGHT
Corpuscular nature Wave nature Dual nature of light
- Advocated by Newton - Dutch physicist C. Huygens - Particle and wave
- Hard - EM Wave - Photons
- Elastic - Hypothetical medium
- Massless - Explain laws

7. LIGHT AS A WAVE
- Light is an electromagnetic wave.
- Reason for formation of spectrum and rainbow.
- Refractive index of a medium depends on the
wavelength used.

8. DO YOU KNOW?
• It was shown by Einstein in his special theory of
relativity that the speed of light (c) does not depend
on the velocity of the source of light or the observer.
He showed that no object or information can travel
faster than the speed of light in vacuum which is
300,000 km/s.
• Waves appear in many forms and shapes. They have
their own properties and behave differently from each
other.

9. Huygens’ Theory
• Primary and secondary sources of light
• Wavefront
• Huygens’ Principle
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ght-and-
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10. Huygens’ Principle
Straight Wavefront: Huygens’s principle applied to a straight wavefront.
Each point on the wavefront emits a semicircular wavelet that moves a
distance s=vt. The new wavefront is a line tangent to the wavelets.

11. Reflection of light at a plane surface
Where, MN: Plane mirror.
RA and QC: Incident rays
AP: Normal to MN
AB: Incident wavefront
i: Angle of incident
CE: Reflected wavefront
R: Angle of reflection
AP is the normal to MN at A.
∠𝑹𝑨𝑷 = 𝒊 and ∠𝑷𝑨𝑬 = 𝒓
In △ 𝑨𝑩𝑪 𝒂𝒏𝒅 △ 𝑨𝑬𝑪,
AE = BC and ∠𝑨𝑩𝑪 = ∠𝑨𝑬𝑪 = 𝟗𝟎𝟎
∴ ∠𝑨𝑪𝑬 = ∠𝑩𝑨𝑪 = i ……(1)
∴ ∠𝑨𝑪𝑬 = ∠𝑷𝑨𝑬 = r ……(2)
i = r
R
P
Q
F
Thus Angle of Incidence = Angle of Reflection. This is the first
law of reflection.
The incident wavefront, the reflected wavefront and normal
lie in the same plane which is perpendicular to the reflecting
surface. This again verifies the second law of reflection.
Therefore, the two Laws of Reflection are verified using
Huygens’s Principle.

12. Reflection of light at a plane surface
Let us assume A and B to be the right and left sides of the object respectively as it
looks into the mirror.
After reflection, the right side, at A is seen at E and the left side at B is seen at C.
As the right side has now become left side and vice-versa as the image comes out of
the mirror. This is called lateral inversion.
• In refraction, when any point of the
incident wavefront interacts with
boundary, secondary waves are
generated and they will have some
velocity.
• Case 1: Rarer medium to denser medium
• Case 2: Denser medium to rarer medium

13. Interference
• Interference is a phenomenon of superposition of 2 waves to form a resultant wave of
greater, lower or the same amplitude.
• When the crest of a wave overlaps the crest of another wave of the same frequency at the
same point, then the resultant amplitude will be the sum of the amplitudes of individual
waves. Then it is known as constructive interference.
• When the crest of one wave meets the trough of another wave, then the resultant amplitude
is given as difference of the two individual amplitudes. Then it is known as destructive
interference.

14. Coherent & Incoherent sources
Coherent Source Incoherent Sources
• Coherent sources are those
sources of light which emit waves
that have same frequency and
zero or constant phase difference

15. Young’s double slit experiment (YDSE)
The Young’s experiment shows that matter and energy can
display both wave and particle characteristics.
Purpose of double slit experiment is as follows:-
1.In order to prove the wave nature of light.
2.To explain the phenomenon of interference.
Conclusion:-
• When coherent sources of light
were taken then the
phenomenon of interference is
taking place.
• When non-coherent sources
were taken phenomenon of
interference was not taking
place.

16. Young’s double slit experiment (YDSE)
Path difference =(xd)/(D)
Observation:-
Light from coherent sources produced alternate dark and
bright bands on the screen placed some distance away from
it.

17. Fringe Pattern
• The alternate dark and red bands which are
obtained on the screen are known as fringe
pattern and the alternate dark and bright bands
are known as fringes.
Graphical representation of fringe pattern

18. Conclusion of Young’s double slit experiment
Central fringes gets shifted by – θ if the source gets shifted by θ.
Problem:- In a Young’s
double-slit experiment,
the slits are separated
by0.28 mm and the
screen is placed 1.4 m
away. The distance
between the central
bright fringe and the
fourth bright fringe is
measured to be 1.2 cm.
Determine the
wavelength of light
used in the experiment.
Ans: The wavelength of
the light is 600 nm.

19. Conditions for Obtaining Well Defined and Steady Interference Pattern:
1. The two sources of light should be coherent.
2. The two sources of light must be monochromatic.
3. The two interfering waves must have the same amplitude.
4. The separation between the two slits must be small in comparison to the distance
between the plane containing the slits and the observing screen.
5. The two slits should be narrow.
6. The two waves should be in the same state of polarization.
Methods for Obtaining Coherent Sources
Lloyd’s mirror Fresnel biprism

20. Optical Path
Optical path in a medium is also defined as the corresponding path in
vacuum that the light travels in the same time as it takes in the given
medium.
Consider, Phase of light wave is (k x – w t)
K = w / v
Similarly, optical path = D ∆ 𝑥
For vacuum actual path travelled (D = 1)
Optical path = ∆ 𝑥
Time = distance / speed
t =
𝑑𝑚𝑒𝑑𝑖𝑢𝑚
𝑣𝑚𝑒𝑑𝑖𝑢𝑚
=
𝑑𝑣𝑎𝑐𝑐𝑢𝑚
𝑣𝑣𝑎𝑐𝑐𝑢𝑚
Optical path = 𝑑𝑣𝑎𝑐𝑐𝑢𝑚 =
𝑣𝑣𝑎𝑐𝑐𝑢𝑚 × 𝑑𝑣𝑎𝑐𝑐𝑢𝑚
𝑣𝑚𝑒𝑑𝑖𝑢𝑚
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21. Diffraction of Light
• Diffraction is another phenomenon of light.
• Diffraction of light occurs when a light wave passes by a corner
or through an opening or slit that is physically the approximate
size of, or even smaller than that lights wavelength.
• Formed when light passes through obstacle and forms the
shadow.
• This phenomenon is applicable for sound wave because
diffraction is wave phenomenon.
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Type of diffraction
Fraunhofer diffraction Fresnel diffraction
Distance between the primary sources of
light, slit causing diffraction and the screen
for viewing the diffraction pattern are very
large.
The distance are much smaller and the
incident wave front is either cylindrical or
spherical depending on the surface.

22. Experimental set up for Fraunhofer diffraction Fraunhofer Diffraction at a Single Slit
In the case of circular aperture, 𝑆 is a point
source and the lenses are bi-convex. For linear
elements like slits, grating etc., the source is
linear and the lenses are cylindrical in shape
so that the focused image is also linear.
Emerging beam is incident on another
converging lens that focuses the beam on a
screen.
According to Huygens’ principle, each and
every point of the slit acts as a source of
secondary wavelets, spreading in all
directions.
• Position of Central Maxima
• Position of secondary minimum
• Position of Secondary Maximum
• Width of the central bright fringe

23. Comparison of Young’s Double Slit Interference Pattern and Single Slit Diffraction Pattern

24. Comparison of Young’s Double Slit Interference Pattern and Single Slit Diffraction Pattern

25. Double slit diffraction pattern
What pattern will be observed due to diffraction from two slits rather than
one? In this case the pattern will be decided by the diffraction pattern of
the individual slits, as well as by the interference between them. The
pattern is shown in figure.
There are narrow interference fringes similar to those in Young’s double slit
experiment, but of varying brightness and the shape of their envelope is
that of the single slit diffraction pattern

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