Question

Thin symmetric prism of $\mu = 1.5$. Find ratio of incident angle and minimum deviation.


 

Answer 1

Step 1: State formulas for a thin prism.
Deviation $\delta_{min} = (\mu - 1)A$.
Angle of incidence at minimum deviation $i = \frac{A + \delta_{min}}{2}$.

Step 2: Express $i$ in terms of $\mu$ and $A$.
$i = \frac{A + (\mu - 1)A}{2} = \frac{\mu A}{2}$.

Step 3: Find the ratio $\frac{i}{\delta_{min}}$.
$\frac{i}{\delta_{min}} = \frac{\mu A / 2}{(\mu - 1)A} = \frac{\mu}{2(\mu - 1)}$.

Step 4: Substitute $\mu = 1.5$.
Ratio = $\frac{1.5}{2(1.5 - 1)} = \frac{1.5}{2 \times 0.5} = \frac{1.5}{1} = 1.5 = \frac{3}{2}$.

Final Answer: 3/2.