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the angle of incidence is equal to the angle of reflection
A formula is something which shows a relationship between two or more things. A formula will contain variables and may also contain constants too and it tells us the relationship between them. The answer to the question is that you square a number if, and only if, the relationship between the variables (or constants) requires the number to be squared. For example in the famous formula e = mc2 , here we must square the constant, the speed of light in a vacuum (c), in order to calculate energy (e). It has to be squared because that constitutes the relationship between the values and there is no option to ignore that.
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Einstein proposed a formula describing the relationship between mass and energy - it is e=mc2 where e is energy, m is mass and c is the speed of light, so the amount of energy (in juoles) is equal to the mass (in Kilograms) multiplied by the speed of light (in metres per second), all multiplied again by the speed of light.
A light beam or beam of light is a narrow cone of light energy radiating from a small source. In optics, a ray is an idealized narrow beam of light.