# Intensity as light passes through two quarter-wave plates?

• Mulz
In summary, a problem concerning the intensity output of polarized light passing through a series of polarizers and quarter-wave plates was discussed. The use of Jones vectors/matrices was suggested as a method for analyzing the problem. The understanding of quarter-wave plates and their effects on polarization was also discussed. An alternative method for determining the intensity output was requested, but the use of Jones calculus was deemed the easiest approach.
Mulz
I have unpolarized light passing through a polarizator assuming the angle 0°. The polarized light then passes through two quarter-wave plates, the first one with the angle of 45° (maximum intensity) and the other one. Then it passes through a last polarizator having an orientation perpendicular to the first polarizator, that is 90°.

What is the intensity output? I don't know how the polarized light behaves when reaching the quarter-wave plates. What angle should the second one be for maximum transmission?

It is in my understanding that quarter-wave plates only causes a phase shift in the electric components, 45° will cause circular polarization and anything else elliptically. Reaching the other should make it linearly polarized. I just don't understand how to calculate the output intensity. I have read that quarter-wave plates does not affect intensity but how come they can cancel each other out then.

Mulz said:
I have unpolarized light passing through a polarizator assuming the angle 0°. The polarized light then passes through two quarter-wave plates, the first one with the angle of 45° (maximum intensity) and the other one. Then it passes through a last polarizator having an orientation perpendicular to the first polarizator, that is 90°.

What is the intensity output? I don't know how the polarized light behaves when reaching the quarter-wave plates. What angle should the second one be for maximum transmission?

It is in my understanding that quarter-wave plates only causes a phase shift in the electric components, 45° will cause circular polarization and anything else elliptically. Reaching the other should make it linearly polarized. I just don't understand how to calculate the output intensity. I have read that quarter-wave plates does not affect intensity but how come they can cancel each other out then.

This type of problem is easily analyzed by using Jones vectors/matrices:

https://en.wikipedia.org/wiki/Jones_calculus

Andy Resnick said:
This type of problem is easily analyzed by using Jones vectors/matrices:

https://en.wikipedia.org/wiki/Jones_calculus
We haven't gone through that.

Is there another way of determining the intensity as it passes through:

Polaroid (0°) → Quarter wave-plate (45°) → Quarter-wave plate (?°) → Polaroid (90°)

The second quarter-wave plate should have an angle in which intensity transmitted total intensity is at maximum. Not sure how to get it.

Mulz said:
We haven't gone through that.

Is there another way of determining the intensity as it passes through:

I'm sure there are other ways, using the Jones calculus is just the easiest. Do you understand what is meant by 'Quarter wave-plate (45°)': what is at 45°? Try thinking about this- what is the polarization state of the light after it passes through the first retarder?

Andy Resnick said:
I'm sure there are other ways, using the Jones calculus is just the easiest. Do you understand what is meant by 'Quarter wave-plate (45°)': what is at 45°? Try thinking about this- what is the polarization state of the light after it passes through the first retarder?

Through the first polaroid it become linearly polarized. I'm not sure what the angle of the quarter-wave plate does. I know that it phase shifts the electric vector components so they oscillate with a 90 degree difference, basically circular polarization. Not sure what 45 degrees does on it.

Anyone?

## 1. What are quarter-wave plates and how do they affect light intensity?

Quarter-wave plates are optical components that are used to manipulate the polarization of light. They are made of birefringent materials, which means they have different refractive indices along different axes. When light passes through a quarter-wave plate, its polarization is altered, resulting in changes in the intensity of the light.

## 2. How does the orientation of quarter-wave plates affect light intensity?

The orientation of quarter-wave plates plays a crucial role in determining the intensity of light passing through them. When two quarter-wave plates are placed perpendicular to each other, they act as a polarizer and analyzer, respectively, and no light passes through. When the plates are oriented at a specific angle, they can produce circularly polarized light, which can have varying intensities depending on the angle.

## 3. What happens when two quarter-wave plates are aligned at the same angle?

When two quarter-wave plates are aligned at the same angle, they produce linearly polarized light. However, the intensity of the light passing through them is affected by the relative phase difference between the two plates. If the plates are perfectly aligned, the intensity of the light will be maximum. If they are slightly misaligned, the intensity will decrease.

## 4. Can quarter-wave plates be used to control the intensity of light?

Yes, quarter-wave plates can be used to control the intensity of light. By adjusting the angle and orientation of the plates, the intensity of light passing through them can be modified. This property of quarter-wave plates is particularly useful in optical devices such as polarimeters, which are used to measure the polarization of light.

## 5. How do quarter-wave plates affect the overall intensity of light passing through them?

Quarter-wave plates do not inherently change the overall intensity of light passing through them. However, the relative orientation and alignment of the plates can affect the intensity of the light. Additionally, if the plates are made of low-quality materials or are not properly aligned, they can introduce losses and decrease the overall intensity of the light passing through them.

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