Match the Column-I with Column-II and choose the correct option :
Column-I : Column-II
(i) Ray through centre of curvature : (A) Reflect parallel rays to principal axis
(ii) Ray through focus : (B) Converges at focus
(iii) Rays from infinite distance : (C) Emerge through focus
(iv) Refracted rays to infinity : (D) Refracting in mirrors

Question

Match the Column-I with Column-II and choose the correct option : 
Column-I : Column-II
(i) Ray through centre of curvature : (A) Reflect parallel rays to principal axis 
(ii) Ray through focus : (B) Converges at focus 
(iii) Rays from infinite distance : (C) Emerge through focus 
(iv) Refracted rays to infinity : (D) Refracting in mirrors

Accepted Answer

To justify why Option 1 is the correct answer, let's analyze each pair in Column-I and Column-II and explain the reasoning behind the matches:

1. **(i) Ray through centre of curvature - (D) Refracting in mirrors:**
   - A ray passing through the center of curvature of a mirror reflects back along the same path. This is because the center of curvature is a point on the principal axis where the mirror's surface is perpendicular to the ray, causing it to reflect directly back. This behavior is characteristic of mirrors, hence the match with (D) Refracting in mirrors.

2. **(ii) Ray through focus - (A) Reflect parallel rays to principal axis:**
   - When a ray passes through the focus of a concave mirror, it reflects and travels parallel to the principal axis. This is a fundamental property of concave mirrors, where rays through the focus reflect parallel to the principal axis. Therefore, the correct match is with (A) Reflect parallel rays to principal axis.

3. **(iii) Rays from infinite distance - (B) Converges at focus:**
   - Rays coming from an infinite distance are essentially parallel to each other. When these parallel rays strike a concave mirror, they converge at the focus. This is a key principle of concave mirrors, making the correct match with (B) Converges at focus.

4. **(iv) Refracted rays to infinity - (C) Emerge through focus:**
   - When rays are refracted such that they appear to be coming from infinity, they effectively emerge through the focus. This is a characteristic behavior in optical systems involving lenses or mirrors, where refracted rays that seem to come from infinity pass through the focus. Thus, the correct match is with (C) Emerge through focus.

Now, let's explain why the other options are incorrect:

- **Option 2: (i) - C, (ii) - D, (iii) - A, (iv) - B**
  - This option incorrectly matches (i) with (C), which does not align with the behavior of rays through the center of curvature. Similarly, (ii) is incorrectly matched with (D), as rays through the focus reflect parallel, not refracting in mirrors. The other matches also do not align with the correct optical principles.

- **Option 3: (i) - B, (ii) - A, (iii) - D, (iv) - C**
  - This option incorrectly matches (i) with (B), which is not the behavior of rays through the center of curvature. Additionally, (iii) is incorrectly matched with (D), as rays from infinite distance converge at the focus, not refracting in mirrors.

- **Option 4: (i) - D, (ii) - B, (iii) - A, (iv) - C**
  - This option incorrectly matches (ii) with (B), as rays through the focus reflect parallel to the principal axis, not converging at the focus. The other matches do not align with the correct optical principles.

In conclusion, Option 1 is the correct answer as it accurately matches each scenario in Column-I with the corresponding behavior in Column-II based on established optical principles.