# Transfer matrix approach Harvard Case Solution & Analysis

## Transfer matrix approach Case Solution

INTRODUCTION

Measuring the reflectance and transmittance of light using matrix approach requires the study of and behavior of light in different medium. Before starting the study of light in different medium, it is required to study the nature of light and spectrum of light.

SPECTRUM OF LIGHT

Light is transvers electromagnetic waves within a portion of electromagnetic spectrum. The wavelength in the range 400-700 nanometer is visible to human eye. This wavelength lies between infrared and ultraviolet. The spectrum of light is shown blow:

[*]Figure Spectrum of Light

What does Physics tell us about light? According to Physics light is an electromagnetic radiation of any wavelength or frequency. Thus, gamma rays, X-rays, ultraviolet rays, infrared rays, radio waves, and shortwaves are also light. The reason behind differentiation of light as gamma rays, X-rays, ultraviolet rays, visible light etc. is due to difference in their behavior. [1]

According to nature of light

The behavior of EMR radiation is explained by wave as well as partial nature of light. The wave nature of light explains diffraction, interference, and polarization, whereas particle nature of light explains reflection, and refraction.

Diffraction

It is the process by which beam of light or any electromagnetic radiation is spread out as a result of passing through narrow aperture or through a sharp edge. [5]

Interference

It is the combination of two coherent electromagnetic waves that results in a new wave caused by the reinforcement or cancelation of the two waves. The reinforcement is called constructive interference and cancelation is called destructive interference. [6]

Polarization

Polarization is the property that describes an electromagnetic wave can oscillate in more than one orientation. Waves such as sound waves and gravitational waves does not exhibit polarization. [7]

Reflection

The law states that angle of incident of light is equal to the angle of reflection of light. The law is based on particle nature of light. [8]

Refraction

Refraction of light is the bending of ray when it passes from one medium to another. When a light ray is passed from faster medium to slower medium the refracted ray bends towards normal, whereas when the light passes from slower to faster medium the refracted ray bends away from normal. [9]

According to property of medium

Let’s explain what is white light? A white light consists of all wavelengths of visible light. This means that, if all the beams of rainbow color are focused at a single spot, it will result in a white color. Thus, a white light consists of seven colors. [2]

Optical material are substances used to control the flow of light. It includes reflection, absorption, splitting, and focusing. [3] Optical material differs from each other by their difference in optical density. Optical density defines the tendency of material to slow down speed of light. As we all know when light travels through transparent medium it interacts with atoms and molecules of the material. This interaction causes the absorption of light by the atom or molecule. The absorbed light causes the electron to vibrate. The vibrating charge, or the accelerating charge produce electromagnetic radiation. [4] The transmission of light through medium depends on the resonance frequency of vibrating electron. If the resonance frequency does not match, then re-emission of light takes place. This light then interacts with the other atom in the substance and the process of absorption and re-emotion repeats.

The optical density is the degree to which refracted medium retards or slowdown the transmitted ray of light. Thus, the speed of light in any transparent medium must be slower than the speed in vacuum.  The index of refraction describes the amount by which a light waves slows down in a transparent medium with respect to the speed of light in vacuum. [10]......................

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