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. If the original light is unpolarized, what should Φ be?

Verified step by step guidance

1. Understand that when unpolarized light passes through a polarizer, its intensity is reduced by half. Therefore, after the first polarizer, the intensity becomes I0/2.
2. Recall Malus's Law, which states that the intensity of polarized light after passing through a second polarizer is given by: $I=I$₀/2⁢cos⁢2φ, where $\phi$ is the angle between the polarizing axes of the two polarizers.
3. Set up the equation using Malus's Law to find the angle $\phi$ such that the intensity at point P is I0/10: $I=I$₀/10. Substitute the intensity after the first polarizer: $I$₀/2⁢cos⁢2φ=I₀/10.
4. Solve the equation for $\phi$: ${\cos }^{}\phi =1/5$. This requires taking the square root and then the inverse cosine.
5. Calculate the angle $\phi$ using the inverse cosine function: $\phi =\cos -1(1/\mathrm{sqrt}(5\left)\right)$. This will give you the angle needed to achieve the desired intensity at point P.

Key Concepts

Polarization of Light

Polarization refers to the orientation of oscillations in light waves. Unpolarized light has oscillations in multiple directions, while polarized light oscillates in a single plane. Polarizing filters can selectively block certain orientations, allowing only light polarized along their axis to pass through.

Malus's Law

Malus's Law describes how the intensity of polarized light changes as it passes through a polarizing filter. It states that the intensity I of light after passing through a filter is given by I = I0 * cos²(Φ), where I0 is the initial intensity and Φ is the angle between the light's polarization direction and the filter's axis.

Intensity Reduction through Filters

When unpolarized light passes through a polarizing filter, its intensity is reduced by half. Subsequent filters further reduce intensity based on Malus's Law. To achieve a specific intensity at point P, the angle Φ must be adjusted to ensure the desired fraction of the original intensity is transmitted.