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∠I+ ∠E= ∠A + ∠D Angle of incidence + angle of emergence = angle of prism (Normally 60°) + angle of deviation. If their sum is not equal,we made personal error in doing an experiment with prism. Please make sense of this equation.

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up vote 4 down vote accepted

The following diagram shows the prism with the incoming and outgoing light rays.

Prism

If you follow the incident light ray in, it gets bent by an angle $\theta_1 = i- r_1$. If you follow the light ray where it leaves the glass, it gets bent again by an angle $\theta_2 = e - r_2$, so the total deviation is:

$$ \begin{align} D &= \theta_1 + \theta_2 \\ &= i + e - (r_1 + r_2) \end{align} $$

For the next step look at the triangle formed by the top of the prism and the light ray, and note that the internal angles must add up to 180°. So:

$$ A + (90 - r_1) + (90 - r_2) = 180 $$

and a quick rearrangement gives:

$$ A = r_1 + r_2 $$

Now substitute for $r_1 + r_2$ in our first equation and we get:

$$ D = i + e - A $$

or:

$$ D + A = i + e $$

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+1, nice answer –  OmnipresentAbsence Mar 12 '13 at 11:09
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Thanks, though sadly I can't claim this is an original answer as you'll come across it in any introductory optics course. –  John Rennie Mar 12 '13 at 11:54
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