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Additionally, would someone explain what contexts it would be appropriate to use this phrase and which contexts is it not appropriate to use this phrase?

A prism is a tool used to break down a problem and look at it in detail. Idiomatically, a prism is a particular piece of information or perspective that one uses to understand something larger.

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Historically, a prism was used to break light up into a spectrum to perform spectral analysis. By breaking up the light emitted or reflected from an object into a spectrum, you can see precisely what the object is made from.

This is a spectrum of the light from our sun. The black lines are called absorption lines. These are wavelengths that are absorbed by the elements in the sun's atmosphere. Since these wavelengths can be precisely mapped to specific elements, you can use a spectral analysis to determine what elements are present in the light.

However, we won't use this idiom when we are referring to something that wasn't changed by perspective- after all, the "looking" part can be changed by tense and the meaning is still the same, however make sure that the idiom comes after the main thing that we are talking about and precedes before what we see through.

These days we use machines called spectrometers to measure spectra more precisely, and there is no need for a human to look directly through a prism; nonetheless, the idiom remains.

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In the phrase "Looking through a prism", the word prism here is being used differently from the prism we use normally (being used metaphorically). Here the prism is being referred to the idea of distortion and different perspectives (as a light would do as it hits a prism), so the idiom is talking about looking at something in a completely different perspective.

This can also mean that someone has been affected by some other influence and by that the person looks at something differently from before. This idiom can also be rephrased as "seen through a prism", "looked through a prism"... etc.

Just a few hours ago, I came across the idiom "through the prism of sth/sb" and looked up said phrase on the internet. I only managed to find one entry entitled "Through The Prism of The Prism?"on englishforums.com.