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The angular radius of an Einstein ring refers to a phenomenon observed in astrophysics where the gravitational field of a massive object distorts the light from a distant object, bending it into a ring-like structure known as an Einstein Ring. This concept is central to the study of gravitational lensing, a phenomenon that is deeply rooted in Einstein's General Theory of Relativity. This tutorial will elaborate on the formula to calculate the angular radius of an Einstein ring, its application, and historical context.

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The formula for calculating the angular radius (θ_{E}) of an Einstein ring is given by:

θ_{E} = √(4GMD/c^{2}d)

Where:

G represents the gravitational constant,

M is the mass of the lensing object,

D is the distance to the lensing object,

d is the distance from the lens to the source object, and

c represents the speed of light.

The formula for the angular radius of an Einstein ring arises from Einstein's General Theory of Relativity, published in 1915. However, it was not until 1936, when Einstein was encouraged by his colleague R.W. Mandl, that he applied this theory to light bending around a massive object, resulting in the concept of the Einstein Ring. The formula has been refined over the years by several physicists and astronomers, including Fritz Zwicky and Maarten Schmidt.

Gravitational lensing, such as that which creates Einstein Rings, is a powerful tool in astrophysics. It allows astronomers to infer the mass of the lensing object, including dark matter which cannot be directly observed. It's also used to magnify distant objects, acting like a natural telescope and enabling us to study galaxies and quasars in the early universe.

Albert Einstein is undoubtedly the key figure in this discipline. His theory of general relativity paved the way for the prediction of phenomena such as gravitational lensing. Fritz Zwicky and Maarten Schmidt also made important contributions to this field, with Zwicky being the first to infer the presence of dark matter through observations of gravitational lensing.

- The first Einstein Ring was observed in 1988 by radio astronomers using the Very Large Array (VLA).
- Gravitational lensing acts as a natural telescope, helping astronomers see objects billions of light-years away.
- The study of Einstein Rings helps astronomers to understand the distribution of dark matter in the universe.

The study of the angular radius of Einstein rings and gravitational lensing at large is fundamental to understanding our universe. It provides key insights into the mass and distribution of galaxies and the mysterious dark matter. The field continues to evolve with the advent of more powerful telescopes, promising new discoveries and breakthroughs in our understanding of the cosmos.

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