CH 1: Nature of light

 Physical optics [wave optics]:

The branch of physics which deals about the study of light on the basis of its wave nature is called as physical
optics.
According to Huygens, source of light sends out waves in all directions through a hypothetical medium (called
ether).
Huygens’ method is a geometrical method.
 Wave- Front and Wavelets:
Wavefront:
Wavefront is the locus (imaginary surface) of all adjacent
vibrating particles of medium which are equidistant from
the source of light and are vibrating in same phase.
Each point in a wavefront vibrating in same phase, which
behave as a source of new smaller spherical wave are called
as wavelets.
The new spherical wave originating from wavefront of the
wave which travels with the speed of wave at that medium is
called wavelet.
 The direction of propagation of light is perpendicular and outward to a wavefront.
 Two wavefronts can never intersect each other.
 The phase difference between any two points on a wavefront is always zero (as they are in same
phase).
Types of Wave-fronts:
Generally, the wave fronts are of three types:
a) Spherical wavefront b) Cylindrical wave front c) Plane wave front
The nature (or type) of wavefront depends upon the nature of source of light and distance of the source from
observer (depends upon nature and distance of light source).
a) Spherical wavefront:
The wavefront of wave produced from a point source is called as spherical wavefront.
The term spherical indicates that the wavefront has spherical surface around and outward the source.
The direction of propagation of wave is perpendicular and outward to the surface of wavefront.
b) Cylindrical wavefront:
The wavefront of wave produced from a linear source is called as cylindrical wavefront.
The term cylindrical indicates that the wavefront has cylindrical surface around and outward the source.
c) Plane wavefront:
The wavefront of wave produced from a distant point or linear source is called as plane wavefront.
The term plane indicates that the wavefront has plane surface reaching the observer

(i) spherical and cylindrical wavefront closer to the source and (ii) plane wavefront far away from the source.
 Remember!!!
 Every point in a wavefront (either spherical, or cylindrical or plane) act like a new point source of light.
These point source are called as wavelets.They travel with speed of light along forward direction.
 The wavefront observed in the ripple (surface of liquid) is a circular wavefront.

Note: We can convert spherical wavefront into plane wavefront and vice-versa.
When a spherical wavefront is kept at the focus of the lens, it changes into plane wavefront. Likewise, if convex
lens is kept in the path of plane wavefront, spherical wavefront is formed.

Conversion of Spherical wavefront to Plane wavefront Conversion of Plane wavefront to Spherical wavefront

Huygens wave theory:

Statement:
According to Huygens, a source of light sends out disturbances (wave) in all directions through a hypothetical
medium called ether. These disturbances travel forward (away from light source) through the medium.
Postulates:
1. Every point on the wavefront become a secondary source of light which spread out in forward direction
at the speed of light.
2. At any given time, a common tangential surface (envelope) on these wavelets in forward direction
form a secondary wavelet.
Explanation:
Consider a spherical wavefront produced by a point source of light. According to Huygens’ principle,
every point on the wavefront [Some points are indicated by dots ( ) in the diagram] behave as the source of
new wave-front and travel with speed of light (𝒄) in forward direction. After time 𝒕, these points spread out
spherically (of radii 𝒄𝒕). The forward tangential envelope over these sphere gives secondary wave-front.
[Note that, there is no backward transmission of energy and hence no backward wave-front.]

1. Which of the following phenomenon cannot be explained by the Huygens wave theory
a. Refraction b. Reflection c. polarization d. interference
2. The locus of all particles vibrating in same phase is called
a. wavelet b. wave front c. vibration d. Huygens’ particle
3. Which of the following parameter of light does not change on refraction
a. Velocity b. wavelength c. frequency d. amplitude
4. Wave nature of light supports best supports
a. Rectilinear light b. Reflection of light c. Interference d. Photoelectric effect
5. If light travels from one medium to another, its velocity changes. This change is due to change in
a. Frequency b. Wavelength c. Mass d. Huygens’ Particle
6. Which of the following parameter of light does not change on refraction
a. Velocity b. Frequency c. Wavelength d. All of above
7. Which of the following principle cannot be explained by wave theory of light
a. Refraction b. Reflection c. polarization d. Photoelectric effect

APPLICATION OF HUYGENS’ PRINCIPLE:

1. Verification of law reflection of light:
The laws of reflection of light are:
I. The incident ray, reflected ray and normal line all lie at same point in a same plane.
II. The angle of incidence is equal to the angle of reflection.

Verification:
Consider two parallel rays of light (in air) incident upon a reflecting surface as shown in figure.
When 𝒓𝒂𝒚 𝑰 reaches to point 𝑨, the 𝒓𝒂𝒚 𝑰𝑰 reaches to point 𝑨′. Hence, 𝑨𝑨’ behave as the incident
wavefront. Similarly, 𝑩𝑩′ behave as reflected wave front.
First law: As shown in figure, the incident ray (𝒓𝒂𝒚 𝑰), the normal line and the reflected ray (𝒓𝒂𝒚 𝑰), all meet
at point 𝑨 on the same plane. This verifies the first law of reflection.
Second law: In the time 𝒓𝒂𝒚 𝑰 travels from point 𝑨 𝑡𝑜 𝑩’, the 𝒓𝒂𝒚 𝑰𝑰 travels from point 𝑨’ 𝑡𝑜 𝑩.
∴ 𝑨𝑩′ = 𝑨’𝑩 = 𝒄𝒕 … … … (1) ; 𝒄 = 𝒔𝒑𝒆𝒆𝒅 𝒐𝒇 𝒍𝒊𝒈𝒉𝒕 𝒊𝒏 𝒂𝒊𝒓.
In figure, in triangles ∆𝐴𝐴′𝐵 and ∆𝐵𝐵′𝐴,
𝐴𝐵 = 𝐴𝐵 ; Being common side
𝐴’𝐵 = 𝐴𝐵′ = 𝑐𝑡 ; Distance travelled by two light rays in same time in same medium.
𝐴𝐴′ = 𝐵𝐵′ ; Remaining sides
Hence, by SSS property these two triangles are congruent.
∴ ∠𝐴′ 𝐴𝐵 = ∠𝐵′𝐵𝐴
𝑖. 𝑒. , 𝒊 = 𝒓 This verifies the second law of reflection of light.

2. Verification of law refraction of light:

The laws of refraction of light are:
I. The incident ray, refracted ray and normal line all lie at same point in a same plane.
II. The ratio of sine of angle of incidence to sine of angle of refraction for a medium is always constant.
𝑺𝒊𝒏 𝒊
𝑖. 𝑒., = 𝑎 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ( 𝝁 )
𝑺𝒊𝒏 𝒓
Verification:
Consider two parallel rays of light (in air) incident upon a refracting surface of refractive index 𝝁, as shown
in figure.
When 𝒓𝒂𝒚 𝑰 reaches to point 𝑨, the 𝒓𝒂𝒚 𝑰𝑰 reaches to point 𝑨′. Hence, 𝑨𝑨’ behave as the incident
wavefront. Similarly, 𝑩𝑩′ behave as refracted wave front.
First law: As shown in figure, the incident ray (𝒓𝒂𝒚 𝑰), the normal line and the refracted ray (𝒓𝒂𝒚 𝑰),
all meet at point 𝑨 on the same plane. This verifies the first law of refraction.
Rough:
Width if incident wavefront = 𝐴𝐴’
Width if refracted wavefront = 𝐵𝐵’

In addition, in the time 𝒓𝒂𝒚 𝑰 travels from point 𝑨 𝑡𝑜 𝑩’ through the medium, the 𝒓𝒂𝒚 𝑰𝑰 travels from
point 𝑨’ 𝑡𝑜 𝑩 in air medium.
∴ 𝑨𝑩′ = 𝒗𝒕 ; 𝒗 = 𝒔𝒑𝒆𝒆𝒅 𝒐𝒇 𝒍𝒊𝒈𝒉𝒕 𝒊𝒏 𝒎𝒆𝒅𝒊𝒖𝒎.
… … … (1)
and, 𝑨’𝑩 = 𝒄𝒕 ; 𝒄 = 𝒔𝒑𝒆𝒆𝒅 𝒐𝒇 𝒍𝒊𝒈𝒉𝒕 𝒊𝒏 𝒂𝒊𝒓.
 Now,
In triangles ∆𝐴𝐴′ 𝐵 𝑎𝑛𝑑 ∆𝐴𝐵′𝐵
𝐴′ 𝐵 𝐴𝐵′
𝑠𝑖𝑛 𝑖 = 𝐴𝐵
and 𝑠𝑖𝑛 𝑟 = 𝐴𝐵
𝒄𝒕 𝒗𝒕
or 𝐬𝐢𝐧 𝒊 = 𝑨𝑩 and 𝐬𝐢𝐧 𝒓 =
𝑨𝑩

𝒔𝒊𝒏 𝒊 𝒄𝒕 𝑨𝑩
Therefore, = ×
𝒔𝒊𝒏 𝒓 𝑨𝑩 𝒗𝒕
𝒔𝒊𝒏 𝒊 𝒄
∴ = = 𝝁 ( 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝒇𝒐𝒓 𝒂 𝒎𝒆𝒅𝒊𝒖𝒎) This verifies the second law of refraction.
𝒔𝒊𝒏 𝒓 𝒗

1. A plane wavefront is incident on a water surface at an angle of incidence 60𝑜 then it gets
refracted at an angle of 45𝑜 .
(i) The ratio of width of incident wavefront to that of refracted wavefront is:
√3 1
a. √2 b. 1.66 c. d.
2 √2
(ii) The refractive index of water is:
3 1
a. √2 b. √1.66 c. √2 d.
√2
2. The wavelength of yellow light in air is 580 𝑛𝑚. The wavelength in diamond of refractive index 2.4 is
a. 200 𝑛𝑚 b. 240 𝑛𝑚 c. 280 𝑛𝑚 d. 320 𝑛𝑚

Exercise:

1. Huygen’s theory is applicable to explain the wave nature of light.

a. Write Huygen’s principle. [1]
b. Verify the laws of reflection using Huygen’s principle. [2]
c. Explain, in brief, how can you convert a spherical wave front into plane wave front. [2]
d. Verify the laws of reflection using Huygen’s principle. [2]
e. What is wavefront? How is spherical wavefront produced? [2]
f. What is wavelet. What is the speed of wavelets? [2]
g. Explain in brief, how is plane wavefront converted into spherical wavefront? [2]