This question involves matching refractive index relationships with ray diagrams for a lens system. The key concept is refraction at curved surfaces and how the path of a light ray bends depending on the refractive indices of the media.

Core Concept: Refraction at a Spherical Surface

When light travels from one medium to another, its path bends. The direction of bending depends on the refractive indices of the two media. The formula governing refraction at a spherical surface is:

Where:

• ${\mu }_1$ is the refractive index of the first medium.
• ${\mu }_2$ is the refractive index of the second medium.
• $u$ is the object distance.
• $v$ is the image distance.
• $R$ is the radius of curvature of the surface.

Rule of Thumb for Bending: Light bends towards the normal when it enters a denser medium (higher refractive index) and away from the normal when it enters a rarer medium (lower refractive index).

Step-by-Step Matching for Column I and Column II

Step 1: Analyze Condition (A) μ₁ < μ₂
This means the ray is moving from a rarer medium (μ₁) to a denser medium (μ₂). Therefore, at the first surface, the ray should bend towards the normal. Look for a diagram where the incident ray, upon entering the lens, bends towards the center of curvature of that surface. This matches the first diagram in Column II.

Step 2: Analyze Condition (B) μ₁ > μ₂
This means the ray is moving from a denser medium (μ₁) to a rarer medium (μ₂). Therefore, at the first surface, the ray should bend away from the normal. Look for a diagram where the incident ray, upon entering the lens, bends away from the center of curvature. This matches the second diagram in Column II.

Step 3: Analyze Condition (C) μ₂ = μ₃
This means the refractive index of the lens material (μ₂) is equal to the refractive index of the medium on the right (μ₃). There is no refraction at the second surface; the ray will pass through undeviated. The entire deviation happens only at the first surface. The ray inside the lens will be a straight line until the second surface, where it continues straight without bending. This matches the fourth diagram in Column II.

Step 4: Analyze Condition (D) μ₂ > μ₃
This means the ray inside the lens (μ₂) is moving towards a rarer medium (μ₃). At the second surface, the ray will bend away from the normal. Look for a diagram where the ray, upon exiting the lens, bends away from the center of curvature of the second surface. This matches the third diagram in Column II.

The fifth diagram shows a ray converging towards the principal axis after refraction, which is a general case and is not exclusively tied to any one specific inequality from Column I. It is often used as a distractor.

Final Answer (Matching)

• (A) μ₁ < μ₂ → Matches Diagram 1
• (B) μ₁ > μ₂ → Matches Diagram 2
• (C) μ₂ = μ₃ → Matches Diagram 4
• (D) μ₂ > μ₃ → Matches Diagram 3

Related Topics & Formulae

Related Topics:

• Refraction at Plane and Spherical Surfaces
• Lens Maker's Formula
• Total Internal Reflection

Key Formula (Lens Maker's Formula):
For a lens with radii of curvature R₁ and R₂, surrounded by a medium of refractive index μ₁, the focal length (f) is given by: $\frac{1}{f}=(\frac{{\mu }_2}{{\mu }_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$ This formula shows how the power of a lens depends on the ratio of the refractive indices of the lens material and the surrounding medium.