Achromatic prism: Why subtract both angles of deflection?

[HastiM]

Hello,

suppose we are given an achromatic prism consisting of two triangular prisms put together as it is shown on this webpage: http://www.schoolphysics.co.uk/age1.../text/Achromatic_prisms_and_lenses/index.html

Imagine a light beam is send through the prism. My book claims that the angle of deflection of the light beam due to the achromatic prism is given by the value δ = δ₁ - δ₂, where δ₁, δ₂ correspond to the angles of deflection of the triangular prisms. That claim is not explained at all, and I would really like to understand why the angles of deflection are just subtracted. Is it possible to deduce this formula from more elementary principles, for example from Snell's law?

I would very appreciate any help!

 

[Baluncore]

One prism bends the ray of light down before the next prism (opposed or inverted) bends the ray of light up again.
The net directional effect is the angular difference of the two prisms.
The subtraction also cancels the chromatic variations, which makes it achromatic.