What is gravitational lensing?
The effects of gravity from celestial bodies help to act as a lens, refracting light similar to how
However, generally, the effects of gravitational lensing are only more significantly observed for light coming from distant objects.
Because gravity can affect the path of light (which travels in a straight line due to the law of rectilinear propagation), as light passes around a celestial object with significant gravity, the path of light is bent as it would be when passing through a thin or thick lens.
Depending on the angle and direction by which light passes by the (let's say) cluster of galaxies, light from (let's say) an even further supernova would be refracted by the gravitational effects of the cluster of galaxies that lie between the distant supernova and observation equipment on Earth.
In fact, the above situation was exactly what happened a few years ago in 2015 - where a group of researchers managed to spot images of a supernova being subjected to heavy gravitational lensing, allowing them to observe the supernova from multiple perspectives in the final moments of its life. Here's an image:
Researchers dubbed it as an "Einstein Cross" after Einstein, who had predicted the effects of gravity being able to act as a lens for light.
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Gravitational lensing is a phenomenon in astrophysics where the light from a distant source is bent and distorted by the gravitational field of a massive object, such as a galaxy or a black hole, in the foreground. This effect can produce multiple images or rings of the source object, and it can also magnify or amplify the light of the source, making it appear brighter. Gravitational lensing provides important information about the distribution of matter in the universe, and it has been used to study dark matter, the properties of distant galaxies, and the structure of the universe itself.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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