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If both angles' terminal rays are in quadrant I, find the values of (a)?

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Final answer:

The question involves calculating light intensity transmission through polarizing sheets in physics. It uses Malus's Law for linear polarization and trigonometric identities for analyzing the effect of orienting polarizing axes at specific angles.

Step-by-step explanation:

The question pertains to the concept of polarization of light in physics and more specifically involves the calculation of light intensity as it passes through polarizing sheets at different angles. For a light incident on a polarizing sheet that is linearly polarized at an angle of 30.0°, the fraction of incident light passing through depends on Malus's Law, I = I0cos²(θ), where I0 is the initial intensity and θ is the angle between the light's polarization direction and the transmission axis of the polarizer. In this case, with the angle at 30.0°, the fraction is cos²(30.0°), which can be calculated using trigonometric functions. For two polarizers with their axes at an angle θ, the intensity, I, of light transmitted can be compared to the intensity, I', when the axes are at an angle 90.0° − θ, involving the identity cos²(θ) + sin²(θ) = 1 to show that I + I' equals the original intensity, I0.

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