Question

An equilateral prism deviates a ray through 40° for two angles of incidence differing by 20°. What can be the possible angles of incidence?

Answer 1

Angle of deviation, d = 40°
Angle of the prism, A = 60°
Let the two angles of incidence be $i_1$
and $(i_2=$ $i_1+20°)$.
When the emergent ray (angle of emergence = e) acts as incident ray, the deviation will be same.
∴ $i_2=e$
Now, D = i + e – A
$\Rightarrow {40}^o=i_1+i_2-A$
$\Rightarrow {40}^o=i_1+i_1+{20}^o-{60}^o$
$\Rightarrow {40}^o=i_1+i_1-{40}^o$
$\Rightarrow 2i_1={80}^o$
$\Rightarrow i_1={40}^o$
$\therefore i_2=i_1+{20}^o$
$={40}^o+{20}^o$
$={60}^o$