Holy Spirit Academy of Malolos
Grade 12
Patience
HSAM SY 2023 2024

Maxwell’s line of reasoning in linking EM to light

According to Maxwell, light is an electric and magnetic field wave that propagates. In a broader sense, he postulated the existence of electromagnetic radiation, which is composed of linked magnetic and electric fields that move at a speed equivalent to the speed of light.


Story behind Hertz’s experiments

The existence of electromagnetic waves was confirmed experimentally by Hertz in 1888. This experiment is based on the fact that oscillating electric charges radiate electromagnetic waves.

Hertz created electromagnetic waves using an induction coil and a Leyden jar, the first capacitor, and utilized an easy handmade laboratory setup to detect them by creating a spark gap between two brass spheres (Edwards, 2012). Since the gaps were hard to notice, he had to conduct his research in a dimly lit space.

It is made up of two metal plates, A and B, spaced 60 centimeters apart. Thick copper wires are used to link the two polished metal spheres, S1 and S2, to the metal plates. A large potential difference is applied across the little space between the spheres using an induction coil. The air in the little space between the spheres becomes ionized due to the large potential difference across S1 and S2, creating a channel for the plate discharge. Between S1 and S2, a spark is created, radiating high-frequency electromagnetic waves.

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Relate the properties of EM wave (wavelength, frequency, speed) and the properties of vacuum and optical medium (permittivity, permeability, and index of refraction)

Properties of EM wave:

The electromagnetic wave is a special kind of wave that can travel through a straight vacuum which means that it does not need any medium. The electric and magnetic fields in an electromagnetic wave are perpendicular to each other along with the direction of the propagation of the wave. Additionally, when it comes to the speed of the electromagnetic wave it travels at a constant speed of 3x10^8 m/s which is similar to the speed of light since the speed of light is an example of an electromagnetic wave. Electromagnetic waves could have any wavelength, the distance between two wave crests or wave troughs, and frequency, the number of wave crests that pass a point per second. In relation to the properties of vacuum and optical medium the two most important constants when it comes to computing the speed are permittivity, the strength of the electric force, and permeability, the strength of the magnetic force, of free space. Moreover, the speed of the em wave changes as the light enters from 1 medium to another specifically due to the index of refraction which talks about the change of direction of light in a medium.


Apply Law of Reflection

To further understand the properties we can apply the law of reflection which is defined as upon the reflection from a smooth surface the angle of the incident ray, the light approaching the smooth surface or specifically the mirror, is equal to the angle of the reflected ray, the ray of light that leaves the mirror. Reflection can have different types such as regular reflection and irregular reflection. It is most likely that smooth surfaces are the one that experiences regular reflection. Irregular reflection, on the other hand, occurs due to the presence of natural surfaces such as rough surfaces which leads to incident light rays being reflected in many different directions.



Conditions for total internal reflection

Total internal reflection occurs when light traveling through a medium encounters a boundary with another medium with a lower refractive index at an angle greater than the critical angle. The critical angle is the angle of incidence beyond which light is completely reflected into the original medium, rather than refracted into the second medium (Admin, 2023). This phenomenon happens when light travels from a more optically dense (higher refractive index) medium to a less dense one (lower refractive index). Total internal reflection is commonly observed in situations like fiber optics, diamond gemstones, and mirages.

Apply Snell’s law

To comprehend the conditions for total internal reflection, we turn to Snell's Law, a fundamental principle governing the behavior of light at the interface between different mediums. Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media and is equal to the ratio of their refractive indices. By applying Snell's Law, we can calculate the critical angle at which total internal reflection occurs. This critical angle is determined by the refractive indices of the two mediums and signifies the threshold beyond which light undergoes total internal reflection rather than refraction. It's expressed as n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two mediums, and θ1 and θ2 are the angles of incidence and refraction, respectively (Admin, 2020b).


What is dispersion?

Dispersion - When passing through an object, white light separates and spreads out based on its respective color and wavelength, creating a spectrum (BYJU’s, n.d., LibreTexts, 2022). It is a property known as dispersion.

The wavelength will determine their angle when passing through a certain material (BYJU’S, n.d.). For instance, the colors of the rainbow have different wavelengths. Red has the longest wavelength while violet has the shortest. The difference between the wavelengths of the colors results in the formation of a rainbow caused by the difference in angles.

What can exhibit dispersion?

Any wave, including sound waves, water waves, and electromagnetic waves, may exhibit dispersion (LibreTexts, 2022; Lumen Learning, n.d.).

Why does dispersion occur?

Dispersion, specifically in rainbows, is determined by refraction (LibreTexts, 2022) based on Snell’s Law, which is the law of refraction (LibreTexts, 2020). Dispersion occurs due to the index of refraction in Snell’s Law.

Other than the angle, different wavelengths also correspond to different indices of refraction of a material. The two variables mentioned, which are the wavelength and index of refraction, are inversely proportional to one another (khanacademymedicine, 2014a). This means that the index of refraction will be smaller if the wavelength is longer and vice versa.

To further understand this concept, kindly watch the video attached below:


Cite evidence that EM wave is a transverse wave (polarization)

Is an electromagnetic wave a transverse wave?

A transverse wave consists of waves that have a perpendicular movement to the direction in which the wave itself is traveling (BYJU’S, n.d.). Transverse waves include ocean waves, secondary earthquake waves, water surface ripples, and electromagnetic waves.

Electromagnetic waves, along with the magnetic field, are a component of electromagnetic radiation or light (BYJU’S, n.d.). This kind of wave is a kind of transverse wave due to polarization. Electromagnetic waves exhibit polarization, which refers to how the electric field lines are oriented compared to the direction the wave is moving (khanacademymedicine, 2014b). It also refers to the transformation of unpolarized light into a polarized one (The Physics Classroom, n.d.).

Just like transverse waves, an electric field oscillates in a vertical plane perpendicular to the direction of wave propagation (khanacademymedicine, 2014b). It is also the case for horizontally polarized waves.

To learn more about electromagnetic waves and polarization, kindly watch the video attached below:


Calculate the intensity of the transmitted light after passing through a series of polarizers applying Malus’s Law

In order to find out the intensity of the transmitted light, the rule of Malus’s Law will be applied. This law states that the intensity of a plane-polarized light depends on the angle between the polarization direction of the light after it passes through an analyzer. This also depends on the transmission axes of the analyzer (BYJUS, n.d.). Following this definition, the formula goes as is:

I = Io cos2 ϕ
where,
I = the intensity of the light transmitted through the analyzer.
Io = the intensity of the incident plane polarized light
Φ = the angle between the axis of polarizer and the analyzer

The theory of Malus’ law comes from the idea that natural light sources, such as Sun, candles, and light bulbs, are unpolarized (Indian Institute of Technology Roorkee, n.d.). An unpolarized light’s electric and magnetic field vectors vibrate in all directions perpendicular to each other and to the direction of the propagation of light.

Unpolarized light

As shown in the diagram, unpolarized light can be represented as a mix of two polarized linear states that are completely uncorrelated. When an unpolarized light passes through an ideal polarizer, the intensity of the light is reduced to half of the incident intensity. During this, the light waves get filtered and produced. Thus, this unpolarized light gets converted into polarized light as shown below:

After the light source passes through a polarizer, it will then encounter an analyzer, which is another polarizing filter oriented at a specific angle Theta degrees relative to the polarizer (Cowen Physics, 2015). If the polarizer and analyzer are aligned, ϕ is zero and the light waves pass through. However, if the polaroid is rotated through 90 degrees, no light would pass through. This behavior is described by the formula of:

A = Ao cos ϕ
where,
A = amplitude of the polarized light
Ao = initial amplitude
Φ = the angle between the axis of polarizer and the analyzer

From this, the intensity of the transmitted light is proportional to the square of the amplitude. Therefore by squaring both sides, the formula gets converted into:

A2 = Ao2 cos2 ϕ —> I = Io cos2 ϕ

Sample Problem

A light source with an intensity of 300 W/m2 passes through a polarizer. It then passes through an analyzer tilted at an angle of 30∘ relative to the polarizer. What is the intensity of the light transmitted through the analyzer?

Solution:
I = (300 W/m2) cos2(30∘)
I = (300 W/m2) (√30/2)2
I = (300 W/m2) (¾)
I = 225 W/m2

Question 1:

Maria wants to find the value of the initial intensity of the light source passing through an analyzer tilted at an angle of 60∘ relative to the polarizer. If the intensity of the light transmitted through the analyzer is equal to 775 W/m2, calculate the initial intensity.

Answer:
775 W/m2 = Io cos2(60∘)
Io = 775 W/m2/ (½)2
Io = 3,100 W/m2

Question 2:

If the initial intensity of the polarized light passing through a polarizer is 100 W/m2, and then it passes through another polarizer tilted at a 30 degree angle relative to the first one, what will be the intensity of light exiting the second polarizer?

Answer:
I = (100 W/m2) cos2(30∘)
I = (100 W/m2) (√30/2)2
I = (100 W/m2) (¾)
I = 75 W/m2
Sources:
BYJU’S. (n.d.). Malus Law - Statement, Experiments, Formula, Important Questions.
BYJU’S. https://byjus.com/jee/malus-law/
Indian Institute of Technology Roorkee. (n.d.). Malus law. Indian Institute of Technology Roorkee.
https://iitr.ac.in/Academics/static/Department/Physics/Optics%20Laboratory/6._Malus_law.pdf.
Cowen Physics. (2015, January 8). Malus’ law. YouTube.
https://www.youtube.com/watch?v=utY72MD-Ii4
Evaluation:
https://quizizz.com/admin/quiz/66347b7d6f469803622d22b4?source=quiz_share

Summary

  • Maxwell's groundbreaking insight: Light is an electromagnetic wave composed of intertwined electric and magnetic fields moving at the speed of light.
  • Hertz's 1888 experiments: Utilized simple apparatus to confirm Maxwell's postulations, solidifying the connection between electromagnetism and light.
  • Properties of electromagnetic waves: Explore characteristics such as wavelength, frequency, and speed, illustrating their interaction with mediums like vacuum and optical materials.
  • Practical applications: Examine phenomena like reflection and refraction, revealing how light behaves in different mediums and surfaces.
  • Additional phenomena: Total internal reflection and dispersion, governed by Snell's Law, provide a further understanding of light wave behavior.
  • Polarization and Malus's Law: Decipher the intensity of transmitted light, demonstrating practical implications in various scenarios.
References

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