D: Wave Optics thx
thx Corpuscular model of light
Descartes gave the corpuscular (particle) model of light. The corpuscular model predicted that if ray of light on
refraction, bends towards the normal, then the speed of light will be greater in the second medium.
thx Wave model of light
Christiaan Huygens put forward the wave theory of light. It predicted that on refraction if the ray of light bends
towards the normal then, the speed of light will be lesser in the second medium.
Note: 1. Wavelength of light is very small as compared to dimensions of typical mirrors and lenses. Therefore, light
can be assumed to travel approximately in a straight line.
2. A ray is defined as the path of energy propagation in the limit of wavelength tending to zero.
3. Light is a transverse electromagnetic wave.
thx Huygens’ Principle (PYQ 2020, 2019,2017, 2013)
Wavefront- A locus of points, all of which of which oscillate in the same phase is called a
wavefront. It is defined as a source of constant phase.
For e.g. When we drop a stone in water, waves spread out from the point of impact
. At any instant, all the points on a circle where disturbance is maximum, oscillate in
the same phase. This is because they are the same distance from the source.
Point source- spherical wavefront
Line source- cylindrical wavefront
Plane source- planar wavefront
Speed of the wave- The speed with which the wavefront moves outwards from
the source is called the speed of the wave. The energy of the wave travels in a
direction perpendicular to the wave front.
Huygens’ Principle-
‘Each point of the wavefront is a source of a secondary disturbance and the wave emanating from these points
spread out in all directions with the speed of the wave. These wavelets emanating from the wavefront are usually
referred to as secondary wavelets and if we draw a common tangent to all these spheres, we obtain the new
position of the wavefront at a later time.’
Thus, if we know the shape of the wavefront at say time t=0 and wish to determine its shape at a later time t=τ, we
draw spheres of radius vτ (where v is speed of the wave) from each point on the wavefront. We then draw a
common tangent to all these spheres and we obtain the new wavefront at t= τ
, Drawbacks of Huygens’ Principle-
To explain the absence of a back wave, Huygens’ argued that the amplitude of the wave is maximum in the forward
direction and zero in the backward direction. But this explanation was not satisfactory.
thx Refraction and Reflection of Plane waves using Huygens’ Principle
1. Refraction of plane wave (at a denser medium) (PYQ 2017)
Let PP’ represent the surface separating medium 1 and 2 (medium 2 is denser). Let v1 and v2 be the speed of light in
medium 1 and 2 respectively. We assume a plane wavefront AB propagating in the direction AA’ incident on the
interface at an angle i. let τ be the time taken by wavefront to travel the distance BC.
From the figure, we can write
Dividing both
From the above equation, we get that if i>r, i.e. the ray bends towards the normal, the speed of light in the second
medium will be less than that inn the first medium i.e. v1>v2. Let c be speed of light in vacuum-
They are known as refractive indices of medium 1 and 2 respectively. We can write-
This is called Snell’s law of refraction. If λ1 and λ2 are the wavelengths of light in the first and second medium, and if
in the fig. BC = λ1, then, the distance AE will be equal to λ2, this is because if the crest has reached C from B in time τ,
then the crest from A should also reach E in the same time (as they are oscillating in the same phase). Thus,
This implies that when a wave gets refracted into a denser medium-
1. Wavelength and speed of propagation decreases
2. Frequency remains the same
2. Refraction at a rarer medium (PYQ 2020, 2019, 2013)
Consider a light wave going from a denser medium to a rare medium. The ray bends away from the normal i.e. r > i.
The speed of light in medium 1 is greater than that in medium 2 i.e. v1<v2. However, we still have the following
equation-
We define the angle ic by the following equation-
Thus, if i=ic then sin r = 1 and r=90°. For i>ic, there will be no refracted wave. The angle ic is known as critical angle.
For all angles of refractions greater than the critical angle, we will not have any refracted and the wave will undergo
what is known as total internal reflection.
thx Corpuscular model of light
Descartes gave the corpuscular (particle) model of light. The corpuscular model predicted that if ray of light on
refraction, bends towards the normal, then the speed of light will be greater in the second medium.
thx Wave model of light
Christiaan Huygens put forward the wave theory of light. It predicted that on refraction if the ray of light bends
towards the normal then, the speed of light will be lesser in the second medium.
Note: 1. Wavelength of light is very small as compared to dimensions of typical mirrors and lenses. Therefore, light
can be assumed to travel approximately in a straight line.
2. A ray is defined as the path of energy propagation in the limit of wavelength tending to zero.
3. Light is a transverse electromagnetic wave.
thx Huygens’ Principle (PYQ 2020, 2019,2017, 2013)
Wavefront- A locus of points, all of which of which oscillate in the same phase is called a
wavefront. It is defined as a source of constant phase.
For e.g. When we drop a stone in water, waves spread out from the point of impact
. At any instant, all the points on a circle where disturbance is maximum, oscillate in
the same phase. This is because they are the same distance from the source.
Point source- spherical wavefront
Line source- cylindrical wavefront
Plane source- planar wavefront
Speed of the wave- The speed with which the wavefront moves outwards from
the source is called the speed of the wave. The energy of the wave travels in a
direction perpendicular to the wave front.
Huygens’ Principle-
‘Each point of the wavefront is a source of a secondary disturbance and the wave emanating from these points
spread out in all directions with the speed of the wave. These wavelets emanating from the wavefront are usually
referred to as secondary wavelets and if we draw a common tangent to all these spheres, we obtain the new
position of the wavefront at a later time.’
Thus, if we know the shape of the wavefront at say time t=0 and wish to determine its shape at a later time t=τ, we
draw spheres of radius vτ (where v is speed of the wave) from each point on the wavefront. We then draw a
common tangent to all these spheres and we obtain the new wavefront at t= τ
, Drawbacks of Huygens’ Principle-
To explain the absence of a back wave, Huygens’ argued that the amplitude of the wave is maximum in the forward
direction and zero in the backward direction. But this explanation was not satisfactory.
thx Refraction and Reflection of Plane waves using Huygens’ Principle
1. Refraction of plane wave (at a denser medium) (PYQ 2017)
Let PP’ represent the surface separating medium 1 and 2 (medium 2 is denser). Let v1 and v2 be the speed of light in
medium 1 and 2 respectively. We assume a plane wavefront AB propagating in the direction AA’ incident on the
interface at an angle i. let τ be the time taken by wavefront to travel the distance BC.
From the figure, we can write
Dividing both
From the above equation, we get that if i>r, i.e. the ray bends towards the normal, the speed of light in the second
medium will be less than that inn the first medium i.e. v1>v2. Let c be speed of light in vacuum-
They are known as refractive indices of medium 1 and 2 respectively. We can write-
This is called Snell’s law of refraction. If λ1 and λ2 are the wavelengths of light in the first and second medium, and if
in the fig. BC = λ1, then, the distance AE will be equal to λ2, this is because if the crest has reached C from B in time τ,
then the crest from A should also reach E in the same time (as they are oscillating in the same phase). Thus,
This implies that when a wave gets refracted into a denser medium-
1. Wavelength and speed of propagation decreases
2. Frequency remains the same
2. Refraction at a rarer medium (PYQ 2020, 2019, 2013)
Consider a light wave going from a denser medium to a rare medium. The ray bends away from the normal i.e. r > i.
The speed of light in medium 1 is greater than that in medium 2 i.e. v1<v2. However, we still have the following
equation-
We define the angle ic by the following equation-
Thus, if i=ic then sin r = 1 and r=90°. For i>ic, there will be no refracted wave. The angle ic is known as critical angle.
For all angles of refractions greater than the critical angle, we will not have any refracted and the wave will undergo
what is known as total internal reflection.
