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Ch 33: The Nature and Propagation of Light
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 33: The Nature and Propagation of LightProblema 25
Capitolo 33, Problema 25

Unpolarized light with intensity I0 is incident on two polarizing filters. The axis of the first filter makes an angle of 60.0° with the vertical, and the axis of the second filter is horizontal. What is the intensity of the light after it has passed through the second filter?

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Start by understanding that unpolarized light has an equal intensity in all directions. When it passes through the first polarizing filter, the intensity is reduced by half. Therefore, the intensity after the first filter is I1 = I0 / 2.
Next, apply Malus's Law to determine the intensity of light after it passes through the second polarizing filter. Malus's Law states that the intensity I after passing through a polarizer is given by I = I1 * cos^2(θ), where θ is the angle between the light's polarization direction and the axis of the polarizer.
In this problem, the angle θ between the light's polarization direction after the first filter (which is at 60.0° to the vertical) and the axis of the second filter (which is horizontal) is 90.0° - 60.0° = 30.0°.
Substitute the values into Malus's Law: I = (I0 / 2) * cos^2(30.0°).
Calculate cos(30.0°), which is √3/2, and then square it to find cos^2(30.0°). Substitute this value back into the equation to find the final intensity of the light after it passes through the second filter.

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Unpolarized Light

Unpolarized light consists of waves vibrating in multiple planes perpendicular to the direction of propagation. When such light encounters a polarizing filter, it becomes polarized, meaning it vibrates in a single plane. The intensity of unpolarized light is reduced by half after passing through the first polarizer, as only the component aligned with the filter's axis is transmitted.
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Ray Nature of Light

Malus's Law

Malus's Law describes how the intensity of polarized light changes as it passes through a second polarizing filter. The transmitted intensity I is given by I = I0 * cos²(θ), where I0 is the initial intensity and θ is the angle between the light's polarization direction and the filter's axis. This law is crucial for calculating the intensity after the second filter in the given problem.
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Multiple Polarizers & Malus's Law

Polarization Angle

The polarization angle is the angle between the polarization direction of light and the axis of a polarizing filter. In the problem, the first filter is at 60° to the vertical, and the second is horizontal, making the effective angle between the polarized light from the first filter and the second filter's axis 30°. This angle is used in Malus's Law to determine the final intensity.
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Introduction to Polarization
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