At a beach the light is generally partially polarized due to...

At a beach the light is generally partially polarized due to reflections off sand and water. At a particular beach on a particular day near sundown, the horizontal component of the electric field vector is $2.3$ times the vertical component. A standing sunbather puts on polarizing sunglasses; the glasses eliminate the horizontal field component. (a) What fraction of the light intensity received before the glasses were put on now reaches the sunbather's eyes? (b) The sunbather, still wearing the glasses, lies on his side. What fraction of the light intensity received before the glasses were put on now reaches his eyes?

Key Concepts

Polarization of Light

Polarization describes the orientation of the electric field oscillations in an electromagnetic wave. In many natural and man?made scenarios, light may become partially or fully polarized due to reflection, transmission, or scattering processes. Understanding polarization is essential for analyzing how light interacts with devices like polarizers, which selectively transmit components of the electric field based on their orientation.

Electric Field Components and Intensity

The electric field of a light wave can be decomposed into orthogonal components, and the light’s intensity is proportional to the square of the amplitude of its electric field. When dealing with partially polarized light or the effect of optical components on the light, it is important to calculate the contributions from each component and how modifications such as filtering one component will affect the overall intensity.

Malus' Law

Malus’ Law provides a quantitative relationship describing how the intensity of polarized light changes when it passes through a polarizer. Specifically, the transmitted intensity is proportional to the cosine squared of the angle between the light’s polarization direction and the axis of the polarizer. This law is a fundamental tool in understanding how orientation affects the transmission of light through polarizing media.

Transmission Through Polarizers

Transmission through polarizers refers to the way in which a polarizing filter selectively absorbs or blocks certain components of the electric field while allowing others to pass. This concept is crucial to understanding how devices like polarizing sunglasses reduce glare by eliminating specific field components, as well as predicting the intensity of light that is transmitted based on the orientation of the light’s initial polarization.

Transcript

0:00 Hi there.

00:02 So for this problem we are given that the horizontal component of the electric field vector it's equal to 2 .3 times the vertical component of the electric field vector.

00:25 Now with this condition and also the information that the glasses eliminate the horizontal field component so that we know that the initial one is a combination, well, the square of the initial one is a combination of the horizontal component square plus the vertical component square.

00:52 But since the glasses eliminate the horizontal field component, then the final electric field square is going to have only the vertical component.

01:10 So with that said, for part a of this problem, we need to find the fraction of the light intensity receive before the glasses were put on and now that the glasses, and now that they are put in the sunbatter's eyes.

01:34 So with that said, we need to calculate the final intensity over the initial intensity.

01:42 Now, the intensity is proportional to the electric field vector.

01:54 Now, we are going to have then that this, well, the square of the electrode field.

02:00 So we are going to have that this is equal to the electric, the, the, final electric fuel square over the initial electric fuel square.

02:11 So we know, as we said from the beginning, that the final one only has the vertical component.

02:25 Meanwhile, the initial one has the horizontal component and the vertical component.

02:32 But we now use the condition that we are given we know that the horizontal component is 2 .3 times the vertical component.

02:46 We elevate that to the squared plus this...

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