Physics Test - 18

• Polarization: This is a process by which unpolarised light is transformed into polarized light.
  • Polarisation tells about the transverse wave nature of light, as the light wave is polarised in a particular plane.
  • The longitudinal waves cannot be polarised.

EXPLANATION:

• Polarization does not work on the Longitudinal wave.
• Only transverse waves can be polarized.
• So, the by the phenomenon of polarization, light shows transverse nature. So the correct answer is option 2.

CONCEPT:

• Interference: When two light sources from different coherent sources meet together, then there is a distribution of energy is disturbed by each other this superposition of two light waves is called Interference of light waves.
• Diffraction: The Phenomena of bending of light the sharp edges of the size of its wavelength is called diffraction.

• Scattering of light: When a parallel beam of light passes through a gas, a part of it appears in direction other than incident direction. This phenomena is called scattering of light.

• Un-polarized light: When in the electromagnetic light the electric field oscillation is not fixed it occur in different orientation/planes then that types of waves are un-polarized. Ex- Sunlight, candle light etc.
• Polarized light: The type of waves having defined oscillations of electric fields. That is polarized light. Ex- The light reflected from water surface etc.
  • Polarization: In this process the electric field vectors of a wave are restricted to single plane by filtration.

• Uniaxial crystal: Uni means one, in this optical elements only one axis is open to pass through.
• Biaxial crystal: Bi means two, in this type of elements only two optical axis are open to pass through.

EXPLANATION:

• Sunlight is an un-polarized type of light, when it passes through a uniaxial crystal it get polarized.

Explanation:

Malus's Law:

The intensity of the transmitted light is directly proportional to the square of the cosine of the angle between the plane of polarization of the light and the transmission axis of the polarizer.

This statement is known as Malus' law (law of malus)

I = I­₀ Cos²θ

Key Points

Initially when a normal light (Unpolarized light) falls on a polarizer, then the intensity of the transmitted light becomes just half of the intensity of the initial light.

CONCEPT:

Unpolarized light:

• A light wave that has vibrations in more than one plane is known as unpolarized light.

Polarized light:

• Polarized light is a light wave in which the vibrations occur in a single plane.

Polarisation by reflection:

• Brewster discovered that when a beam of unpolarized light is reflected from a transparent medium, then at a certain angle of incidence the reflected light will be completely plane polarised.
• The angle of incidence at which the light becomes polarised is called the angle of polarisation.

Brewster's law:

• According to Brewster's law, the refractive index of the medium is numerically equal to the tangent angle of polarization.

​⇒ μ = tanθ_P

• When the reflected light is completely polarised, then the angle between the reflected and the refracted light is 90°.

Where μ = refractive index and θ_P = polarization angle

EXPLANATION:

• According to Brewster's law, if the reflected light is completely polarised, then the angle between the reflected and the refracted light is 90°.
• Hence, option 2 is correct.

• When light is scattered in the atmosphere, the amount of scatter and the angle by which it is scattered depends on the wavelength and the size of the scatterer.
• If you look away from the sun, blue light traveling from the sun through the earth’s atmosphere (but not directly toward you) is scattered by the molecules toward your eye.
• Thus the sky looks blue because scattering from molecules is much more probable for blue light than red.

• As the white light from the Sun enters Earth’s atmosphere, much of the red, yellow, and green wavelengths of light (mixed together and still nearly white) pass straight through the atmosphere to our eyes.
• The blue and violet waves, however, are just the right size to hit and bounce off of the molecules of gas in the atmosphere.
• This causes the blue and violet waves to be separated from the rest of the light and become scattered in every direction for all to see.
• The other wavelengths stick together as a group and therefore remain white.

\(Scattering \propto \frac{1}{{{\lambda ^4}}}\)

CONCEPT:

• The angle of incidence at which a beam of unpolarized light falling on a transparent surface is reflected as a beam of completely plane polarised light is called polarising or Brewster angle. It is denoted by ip.
• Brewster's law: It states that when a ray is passed through some transparent medium having refractive index μ at any particular angle of incidence, the reflected ray is completely polarized; and the angle between reflected and refracted ray is 900.

​

⇒ μ = tan θB 

Where μ = refractive index and θB is Brewster's angle or polarizing angle (ip).

EXPLANATION:

• The unpolarized light has two electric field components, one perpendicular to the plane of incidence (represented by dots) and the other in the plane of incidence (represented by arrows).
• When an unpolarized light beam is an incident from the air onto glass (n = 1.5) at the polarizing angle (i_p), most of these vibrations of electric vector get transmitted and are not reflected. Hence light refracted is a mixture of polarized light and unpolarized light. i.e., it is partially polarized.
• The reflected light, therefore, contains vibrations of an electric vector perpendicular to the plane of incidence.
• Hence the reflected light is completely plane-polarized in a direction perpendicular to the plane of incidence and thus reflected beam is polarized 100 percent.

As unpolarized light passes through first filter, only components of light which have planes parallel to filters axis will get passed. Now after first filter polarized light E will act as light source for second filter. At this time there is no polarization because filter axis and component of light have parallel plane and all the polarized light passed by the first filter is also passed by the second.

Concept:

• The angle of incidence at which a beam of unpolarized light falling on a transparent surface is reflected as a beam of completely plane polarised light is called polarising or Brewster angle. It is denoted by ip.
• Brewster's law: It states that when a ray is passed through some transparent medium having refractive index μ at any particular angle of incidence, the reflected ray is completely polarized; and the angle between reflected and refracted ray is 900.

​

 μ = tan θB 

Where μ = refractive index and θB is Brewster's angle or polarizing angle (ip).

​Calculation:

Given that:

The light is incident on glass

The refractive index of glass (μ) = 3/2

The angle of incidence (ip) = ?

\({3\over2} =tan\;θ ⇒ θ = tan^{-1} ({3\over2})\)

Concept:

Polarization: The transverse light waves create vibration in more than one phase. The polarization is done to make these vibrations confined in one phase.

• Polaroid: A polaroid converts unpolarized light into polarized lights. It acts as a filter that filters out other phases except 1.
• When the polaroid is kept perpendicular to the surface then the intensity of resultant polarized light becomes half.
• Mauss Law: When there is a second polarizer tilted at angle θ  then the intensity obtained from the output of the polarizer will be 

I = I₀ cos² θ 

Calculation:

The given the intensity of polarized light is I₀

Light rays obtained from the output of the first polarizer get intensity reduced to half. So, the intensity obtained from the first polarizer is 

\(I' = \frac{I_0}{2}\) -- (1)

Intensity obtained from the second polarizer which is tilted at angle θ is (By Mauss Law)

I''  = I' cos ² θ  

But the intensity of the final obtained light is I0 / 4, So we can say

\(\frac{I_0}{4}= I'cos^2 θ \) -- (2)

Using (1) in (2)

\(\frac{I_0}{4}= \frac{I_0}{2} cos^2 θ \)

\( cos^2 θ = \frac{1}{2}\)

\(cos θ = \frac{1}{\sqrt{2}}\)

θ = 45 ° 

So, 45 ° is the correct answer.

Concept:

Brewster angle –

• The angle of incidence at which a beam of unpolarized light falling on a transparent surface is reflected as a beam of completely plane polarised light is called polarising or Brewster angle. It is denoted by ip.
• The British Physicist David Brewster found the relationship between Brewster angle (ip) and refractive index (μ) –
  μ = tan ip

Note: It is implicit in the above formula that the first medium is air and the second medium has a refractive index of μ. 
Calculation:

As reflected light is completely polarized, therefore,

i_p = 60°

\(μ = \tan {i_p} = \tan 60^\circ = \sqrt 3 \)

As \(μ = \frac{c}{v}\)

∴ \(v = \frac{c}{μ } = \frac{{3 \;\times\; {{10}^8}}}{{\sqrt 3 }}\)

= \(\sqrt 3 \times {10^8}\;m{s^{ - 1}}\)