Question

For a prism of angle \(5^\circ\), the angle of minimum deviation \((\delta)\) varies with refractive index \((\mu)\) as shown in the graph. The slope of the graph is: center

center

• A. \(5^\circ\)
• B. \(5\,\text{rad}\)
• C. \(0.5^\circ\)
• D. \(0.5\,\text{rad}\)

Hint:

For a thin prism: \[ \delta=(\mu-1)A \] Therefore graph between \(\delta\) and \(\mu\) is always a straight line with slope equal to prism angle.

Answer 1

The Correct Option is A

Step 1: Use the thin prism formula.
For a thin prism the deviation is \[ \delta = (\mu - 1)A \] where $\mu$ is the refractive index and $A$ is the prism angle.

Step 2: Rearrange into a straight line form.
Expand the bracket so $\mu$ appears on its own. \[ \delta = A\mu - A \]
Step 3: Compare with a line equation.
A straight line is $y = mx + c$. Here $\delta$ plays the role of $y$ and $\mu$ plays the role of $x$.
Step 4: Read off the slope.
The number sitting in front of $\mu$ is the slope. \[ m = A \]
Step 5: Put in the prism angle.
The given angle is $A = 5^\circ$.
Step 6: State the slope.
So the slope of the graph is \[ \boxed{5^\circ} \]