#### Question

Find the angle of incidence at face AB so that the emergent ray grazes along the face AC.

#### Solution

from snell's law we know that

`sini/sinr =μ_(12)`

For the emergent ray to graze at the face AC, the angle of refraction should be 90°.

So, applying snell's law at face AC, we get `(sini_(AC)/sinr_(AC) )= μ_(21)`

`⇒ (sin i_(AC)/sin 90^@)=1/sqrt2 or i_(AC)= 45°.`

From geometry we can see that angle of refraction at face AB is 15°.

So applying snell's law we get `(sin i_(AB)/sin r_(AB))= μ_(12)`

`or sin i_(AB) = sin r_(AB)×μ_(12)`

`or i_(AB) =sin^-1(sqrt2sin15°)`

Is there an error in this question or solution?

Solution Find the angle of incidence at face AB so that the emergent ray grazes along the face AC. Concept: Refraction Through a Prism.