Question

The Brewsters angle $i_b$ for an interface should be:

• A. \(0< i b < 30\)
• B. \(30< i_b < 45\)
• C. \(45< i_b < 90\)
• D. \(i_b = 90\)

Answer 1

The Correct Option is C

The Brewster's angle, denoted as \(i_b\), is the angle of incidence at which light with a particular polarization is perfectly transmitted through a surface without any reflection. It occurs when the reflected and refracted light rays are at 90° to each other.

The formula for Brewster's angle is given by:

\(i_b = \arctan\left(\frac{n_2}{n_1}\right)\)

where:

• \(n_1\) is the refractive index of the initial medium,
• \(n_2\) is the refractive index of the second medium.

Brewster's angle is typically greater than 45° for most materials when air is one of the media involved. This is especially true when going from air into a medium like glass or water, as these have refractive indices greater than 1. Therefore, Brewster's angles for common materials like glass and water are usually in the range between 50° to 60°.

Let's consider common values:

• For air to glass (\(n_2 \approx 1.5\)): \(i_b = \arctan(1.5) \approx 56.3°\)
• For air to water (\(n_2 \approx 1.33\)): \(i_b = \arctan(1.33) \approx 53.1°\)

Given the options and understanding the typical range of Brewster's angle for standard cases such as air-glass or air-water interfaces, the correct answer is:

\(45< i_b < 90\)

This range correctly places Brewster's angle for these scenarios, indicating option 3 is the correct choice.