Question

An equilateral prism deviates a ray through $45°$ for the two angles of incidence differing by $20°$. What is the angle of incidence?

Answer 1

Step (1) Given:

Angle of deviation, $d=45°$

Difference between the angles of incidence, $angleofincidence-angleofemergence=20°$

Step (2) Finding the relation between the angles of incidence:

Let the initial and final angles of incidence (angle of incidence and angle of emergence) be $i_{1}and{i}_2$

From given,

$$\begin{gathered} i_1-i_2=20° \\ {i}_1+20°=i_2 \end{gathered}$$

Step (3) Finding the initial angle of incidence:

We know that

$$\begin{gathered} d=i_1+i_2-A \\ bysubstitutingthecorrespondingvalues,weget \\ 45=i_1+(i_1+20)-60 \\ \Rightarrow 45=2i_1-40 \\ \Rightarrow 45+40=2i_1 \\ \Rightarrow 85=2i_1 \\ \Rightarrow 42.5=i_1 \end{gathered}$$

Step (4) Finding the final angle of incidence:

$$\begin{gathered} i_1+20°=i_2 \\ \Rightarrow 42.5+20=i_2 \\ \Rightarrow 62.5°=i_2 \end{gathered}$$

Therefore, the angle of incidence is $62.5°$