What happens when the two faces of the medium are not parallel to each other i.e. in case of prisms ?

A ray of light striking at one face of prism gets refracted twice and emerges out from the other side as shown in the above figure. The angle between the emergent and the incident rays is called the angle of deviation and the angle between the two refracting faces is called the angle of the prism (or refracting angle).

### Refraction through a prism

The incident ray first gets refracted at L . Snell’s law of refraction yields,

$ \displaystyle \frac{sin i_1}{sin r_1} = n $

$ \displaystyle sin r_1 = \frac{sin i_1}{n} $

$ \displaystyle r_1 = sin^{-1} (\frac{sin i_1}{n}) $

Then the refracted ray again gets refracted at M.

Applying Snell’s law we obtain

$ \displaystyle \frac{sin r_2}{sin i_2} = \frac{1}{n} $

$ \displaystyle sin i_2 = n(sin r_2) $

$ \displaystyle i_2 = sin^{-1}(n sin r_2) $

In Quadrilateral ALOM , ∠L + ∠M = 180

Hence , ∠O + ∠A = 180 ..(i)

In Triangle OLM ,

∠O + r_{1} + r_{2} = 180 …(ii)

From (i) & (ii)

⇒ (r_{1} + r_{2}) = A ………..(iii)

### Angle of Deviation

The angle of deviation can be given as

δ = ∠PLM + ∠PML

⇒ δ = (i_{1} − r_{1}) + (i_{2} − r_{2})

⇒ δ = (i_{1} + i_{2}) − (r_{1} + r_{2})

Putting r_{1} + r_{2} = A we obtain

δ = i_{1} + i_{2} − A