Understanding Polarization: How an Oblique Polarizer Makes Two Perpendicular Polarizers Transparent

The world of physics, particularly optics, is fascinating with myriad phenomena. One such interesting case is the behavior of polarized light when placed between two perpendicular polarizers. By introducing a third polarizer at an oblique angle, we can achieve a fascinating result: making the interface between two perpendicular polarizers appear transparent. Let's delve into the intricacies of this phenomenon.

Polarized Light: The Foundation

When light travels, it oscillates in all directions. Polarized light is a special case where this oscillation is restricted to a single plane. This property is achieved when the light passes through a polarizer, which selectively allows light with a specific vibration direction (plane of polarization) to pass through.

Two Perpendicular Polarizers: Blocking Light

Imagine two polarizers positioned perpendicular to each other. One polarizer is oriented at 0 degrees, allowing light with that polarization to pass. The second polarizer is oriented at 90 degrees, meaning it blocks light with the polarization aligned with the first polarizer's transmission axis. Consequently, when light is shone between these two polarizers, it gets blocked, leading to a dark interface between them.

Introducing an Oblique Polarizer: The Key to Transparency

To address the issue of the two polarizers blocking the light, a third polarizer is introduced at an oblique angle, typically 45 degrees, between the two perpendicular polarizers. This setup leverages the principle of Malus's Law to allow some light to pass through. Here's how it works step-by-step:

Step 1: Light Through the First Polarizer

When unpolarized light passes through the first polarizer, it becomes polarized with its electric field oscillating along the transmission axis of the polarizer. In this case, the light is polarized at 0 degrees.

Step 2: Passing Through the Oblique Polarizer

The polarized light at 0 degrees then passes through the oblique polarizer at 45 degrees. Using Malus's Law, the transmitted intensity (I) is given by the formula:

I I_0 cos^2 theta

where (I_0) is the initial light intensity and (theta) is the angle between the polarization direction and the polarizer's axis. Here, (theta 45) degrees, thus:

I I_0 cos^2(45) frac{I_0}{2}

This means that half of the light intensity is transmitted through the 45-degree polarizer.

After passing through the 45-degree polarizer, the light has a polarization angle of 45 degrees.

Step 3: Passing Through the Second Polarizer

Finally, this now polarized light (45 degrees) passes through the second polarizer, which is still at 90 degrees. Contrary to the expectation of complete blockage, some of the light can still pass through. This is due to the tilt of the 45-degree polarizer, which is enough to allow a significant portion of light to pass without being fully blocked.

Conclusion: Achieving Transparency

Through the strategic introduction of the 45-degree oblique polarizer, the system appears transparent. The oblique polarizer serves as a bridge, changing the polarization direction of the light, such that it can pass through the system.

This phenomenon is fascinating as it demonstrates how simple adjustments in the orientation of polarizers can lead to significant changes in light behavior, ultimately achieving transparency where it would otherwise be blocked.

Conclusion and References

The ability to manipulate light through polarizers has numerous practical applications, from 3D movies to sunglass technology. Understanding the principles behind these interactions is crucial for advancements in fields such as optics, photonics, and even the development of new technologies.

References:

Malus, J.B.L. (1809). ldquo;Memoir sur la reflexion des rayons homogenes,rdquo; Annales de chimie et de physique, 2nd series 2, pp. 158-171. Burnham, Jim (2017). ldquo;The Physics Classroomrdquo;. Hecht, Eugene (2017). ldquo;Opticsrdquo; (5th ed.). Boston: Bostock, M.