Consider OP is the incidence ray, which is making the angle i₁ with normal, and QR is the emergent ray making an angle of emergence, i₂ with the normal. A is the prism angle and n is the refractive index of the prism.

The angle of minimum deviation (δ) is the smallest angle of deviation that a prism can produce for a particular wavelength of light. It occurs when the incident ray inside the prism is refracted at the first surface, undergoes minimum deviation inside the prism, and then refracts again at the second surface, emerging parallel to its incident direction.

In the case of minimum deviation, ∠r₁=∠r₂=∠r

Also, we’ve A = ∠r₁ + ∠r₂

so, A = ∠r + ∠r = ∠2r

Now, again,

A + δ = i₁ + i₂  

But in the case of minimum deviation, i₁ = i₂ = i,

So, A + δ = i + i = 2i  …. (1)

So from snell's law, we have,

Again from (1), we can write, A + δ = 2i, so the above equation becomes,

This is the equation for the angle of prism, A.