With reference to the figure shown below, match the following:
Show Hint
The angle of deviation $\delta$ is effectively the "turn" the light takes. If it strikes at $30^{\circ}$ and reflects at $30^{\circ}$, it has changed direction by $180^{\circ}$ minus the total angle between the rays ($60^{\circ}$), resulting in $120^{\circ}$. \
Step 1: Understanding the Question:
This question requires applying the basic laws of reflection at a plane mirror and understanding geometric optics terms like angle of reflection, glancing angle, and angle of deviation. \
Step 2: Key Formula or Approach:
1. Law of Reflection: Angle of incidence ($i$) = Angle of reflection ($r$). \
2. Normal Geometry: The normal is perpendicular to the mirror surface. Glancing angle ($\alpha$) = $90^{\circ} - r$. \
3. Angle of Deviation ($\delta$): The angle through which the incident ray is turned after reflection. For a single reflection, $\delta = 180^{\circ} - 2i$ or $180^{\circ} - (i+r)$. \
Step 3: Detailed Explanation:
From the given figure: \
- The incident ray makes an angle of $30^{\circ}$ with the normal. Thus, Angle of incidence $i = 30^{\circ}$. \
- (a) Angle of reflection ($r$): By the law of reflection, $r = i = 30^{\circ}$. This matches with (iii).
- (b) Value of $\alpha$: $\alpha$ is the angle between the reflected ray and the mirror surface. Since the angle between the normal and the mirror is $90^{\circ}$, $\alpha = 90^{\circ} - r = 90^{\circ} - 30^{\circ} = 60^{\circ}$. This matches with (i).
- (c) Angle of deviation ($\delta$): The deviation is $\delta = 180^{\circ} - 2i = 180^{\circ} - 2(30^{\circ}) = 180^{\circ} - 60^{\circ} = 120^{\circ}$. This matches with (ii).
Combining these: a - iii, b - i, c - ii. Step 4: Final Answer:
The correct matching corresponds to code (3). \
