Light of original intensity I0 passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.28. You want to adjust the angle f so that the intensity at point P is equal to I0/10. (b) If the original light is linearly polarized in the same direction as the polarizing axis of the first polarizer the light reaches, what should Φ be?

Verified step by step guidance

1. Understand that when light passes through a polarizer, the intensity of the light is reduced according to Malus's Law, which states that the intensity I after passing through a polarizer is given by I = I0 * cos^2(θ), where θ is the angle between the light's initial polarization direction and the axis of the polarizer.
2. Since the light is initially polarized in the same direction as the first polarizer, the intensity after the first polarizer remains I0 because cos(0) = 1.
3. For the second polarizer, the angle between the light's polarization direction (after the first polarizer) and the second polarizer's axis is Φ. According to Malus's Law, the intensity after the second polarizer is I = I0 * cos^2(Φ).
4. Set the intensity after the second polarizer equal to I0/10, as given in the problem. This gives the equation I0 * cos^2(Φ) = I0/10.
5. Solve the equation cos^2(Φ) = 1/10 to find the angle Φ. This involves taking the square root of both sides and then finding the angle whose cosine gives the result.

Key Concepts

Polarization of Light

Polarization refers to the orientation of the oscillations of light waves. In linearly polarized light, the electric field oscillates in a single plane. Polarizers are optical filters that allow light waves of a specific polarization to pass through while blocking others, thus reducing the intensity of unpolarized light by half when aligned with the light's polarization direction.

Malus's Law

Malus's Law describes how the intensity of polarized light changes as it passes through a polarizing filter. The law states that the transmitted intensity I is given by I = I0 * cos²(Φ), where I0 is the initial intensity and Φ is the angle between the light's initial polarization direction and the axis of the polarizer. This principle is crucial for calculating the intensity after passing through multiple polarizers.

Angle of Polarization

The angle of polarization, Φ, is the angle between the direction of the incoming polarized light and the axis of the polarizer. Adjusting this angle affects the intensity of the transmitted light according to Malus's Law. In this problem, finding the correct angle Φ is essential to achieve the desired intensity of I0/10 at point P, given the initial polarization alignment with the first polarizer.