# Why does the free end refraction occur after Brewster's angle in TM?

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• jojoe
In summary, the conversation discusses the phenomenon of free end reflection in TM waves at angles greater than the Brewster Angle. It is explained that at these angles, the reflected wave undergoes a 180 degree phase shift, resulting in cancellation between the incident and reflected waves. The concept of free end reflection is further explored, with the suggestion that it can be represented by the summation of a free end reflection term and a fixed end reflection term. The relationship between free end reflection and cancellation is also discussed.
jojoe
Thanks for reading my question, and i’m really sorry about my poor english.

What i am wondering about is
why does the free end occur after the incidence angle overcome the Brewster angle in TM wave? (The ray incident from vacuum to glass(dense medium))

i tried to interpret this phenomenon with dipole oscillation of medium and the velocity difference of light in different medium(with more detail, vacuum to dense medium), but those trial didn’t make any effective conclusions.

Could someone help me about understanding this with macro or microscale aspect?

Last edited:
Sorry Jojoe, can you try to find another word for free end as I cannot understand it.
At angles greater than the Brewster Angle, the reflected wave undergoes a 180 deg phase shift. At angles less than the Brewster Angle it does not. This phase shift at large angles of incidence can result in cancellation between incident and reflected waves.

tech99 said:
Sorry Jojoe, can you try to find another word for free end as I cannot understand it.
At angles greater than the Brewster Angle, the reflected wave undergoes a 180 deg phase shift. At angles less than the Brewster Angle it does not. This phase shift at large angles of incidence can result in cancellation between incident and reflected waves.
I think free end reflection might be proper representation, that the reflected light has the same phase with incident light. I thought about some idea that the reflection coefficient can be represented with the summation of free end reflection term(which has positive sign with cosine) and fixed end reflection term(which has negative sign of sine in sqrt). As the angle gets greater than Brewster angle, the free end reflection term is dominant, so the whole reflection terms gets positive value, which designates free end reflection of TM wave. Will it be related with the cancellation between the incident and reflected waves?

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Thank you, I understand now. I think you are correct. Cancellation occurs if the detector sees both the incident beam of light and the reflected beam of light for the case when angle of incidence is greater than the Brerwster Angle.

## 1. Why does the free end refraction occur after Brewster's angle in TM?

The free end refraction occurs after Brewster's angle in TM because at Brewster's angle, the incident light is polarized parallel to the refracted light. This means that the electric field of the incident light is perpendicular to the plane of incidence. However, as the angle of incidence increases, the electric field becomes more and more parallel to the plane of incidence. This results in a change in the polarization of the refracted light, causing the free end refraction.

## 2. What is Brewster's angle in TM?

Brewster's angle in TM, also known as the polarizing angle, is the angle of incidence at which the reflected light is completely polarized parallel to the plane of incidence. This means that the electric field of the incident light is perpendicular to the plane of incidence.

## 3. How does the polarization of light affect the free end refraction?

The polarization of light plays a crucial role in the occurrence of the free end refraction. As mentioned earlier, at Brewster's angle, the incident light is polarized parallel to the refracted light. As the angle of incidence increases, the polarization of the refracted light changes, leading to the free end refraction.

## 4. Is the free end refraction only observed in TM polarization?

No, the free end refraction can also occur in other polarizations, such as TE (transverse electric) polarization. However, it is most commonly observed in TM polarization due to the specific conditions required for it to occur.

## 5. What are the practical applications of understanding the free end refraction after Brewster's angle in TM?

Understanding the free end refraction after Brewster's angle in TM is crucial in various fields, such as optics, telecommunications, and material science. It allows for the manipulation and control of light in devices such as polarizers, waveplates, and optical fibers. It also helps in the study and analysis of the properties of different materials and their interactions with light.

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