Question

A source of light \(\left(f=6.0 \times 10^{14} \mathrm{Hz}\right)\) passes through three plane polarizers. The first two polarizers are in the same direction, while the third is rotated \(90^{\circ}\) with respect to the second polarizer. What is the frequency of the light that comes out of the third polarizer? (A) \(3.0 \times 10^{14} \mathrm{Hz}\) (B) \(6.0 \times 10^{14} \mathrm{Hz}\) (C) \(9.0 \times 10^{14} \mathrm{Hz}\) (D) Light will not pass through the third polarizer

Short answer

(D) Light will not pass through the third polarizer

Step-by-step solution

Understand the Problem

We have a light source with a frequency of \( f = 6.0 \times 10^{14} \, \mathrm{Hz} \). This light passes through three polarizers. The first two polarizers are aligned in the same direction, and the third polarizer is perpendicular \( (90^{\circ} \) to the second. We need to determine the frequency of the light emerging from the third polarizer.

Recall Polarizer Effects on Light

A polarizer only changes the amplitude (intensity) of the light passing through it, not its frequency. Therefore, irrespective of the orientation, the frequency of light passing through any number of polarizers remains the same.

Analyze the Configuration of the Polarizers

Since the frequency remains unchanged by the polarizers' orientation, the critical aspect is the alignment. Light passing through aligned polarizers retains its polarization direction and frequency.

Evaluate the Effect of the 90-degree Rotation

When light encounters the third polarizer, which is rotated by \( 90^{\circ} \) relative to the second, the direction of polarization fully blocks the light. This means no light passes through this setup.

Conclusion

Given that no light can pass through the third polarizer due to perpendicular orientation, the final frequency is irrelevant since there is no emergent light.

Key concepts

polarization of light

Light waves are electromagnetic waves that can vibrate in many directions. When light passes through a polarizer, it only allows waves vibrating in one direction to pass through. This process is known as polarization. You can think of a polarizer as a filter that blocks certain directions of vibration, much like how a picket fence only allows things through that are oriented in the same direction as the gaps.

When light passes through the first polarizer, it becomes polarized in the direction of that polarizer. If the light then passes through a second polarizer aligned in the same direction, it will still pass through.

• Light before the first polarizer is unpolarized.
• Light after the first polarizer is polarized in one direction.

If a third polarizer is introduced at an angle different from the first two, it will block some or all of the light, depending on the angle.

frequency of light

The frequency of light is a measure of how many waves pass a point in one second. It is measured in Hertz (Hz). For example, in the exercise provided, the light has a frequency of \( f = 6.0 \times 10^{14} \mathrm{Hz} \).

An important point to understand is that the frequency of light is an inherent property of the light wave itself. It does not change when light passes through a medium, including a polarizer. What polarizers affect is the direction and amplitude (intensity) of the light, not its frequency. This means:

• Before the first polarizer: frequency of light is the same.
• After passing through any number of polarizers: frequency remains unchanged.

So, even when light encounters different orientations of polarizers, its frequency does not alter.

polarizer orientation effect

The orientation of a polarizer relative to the previous one is critical in determining the amount of light that passes through. In this exercise, the first two polarizers are aligned; thus, the polarized light from the first will pass through the second with minimal intensity loss. However, the third polarizer is turned \( 90^{\circ} \) relative to the second.

When a polarizer is rotated \( 90^{\circ} \) (perpendicular), it blocks all light polarized by the previous polarizer. This angular difference ensures no light passes through. To summarize:

• Two polarizers aligned in the same direction: light passes through with reduced intensity.
• Third polarizer rotated \( 90^{\circ} \) relative to the second: light is completely blocked.

Therefore, no light emerges from this polarizer setup, and the frequency of the light is rendered irrelevant as no light exits.