A ray falls on a prism of angle 55° and refractive index 1.52, at an angle of incidence of 45°…

Step 1. First face. $\sin r_1 = \dfrac{\sin 45^\circ}{1.52} = \dfrac{0.707}{1.52} = 0.465$, so $r_1 = 27.7^\circ$.

Step 2. Inside. $r_2 = 55^\circ - 27.7^\circ = 27.3^\circ$.

Step 3. Second face. $\sin e = 1.52 \times \sin 27.3^\circ = 0.697$, so $e = 44.2^\circ$.

Step 4. Deviation. $\delta = 45^\circ + 44.2^\circ - 55^\circ = 34.2^\circ$.