Concept Explanation: Refraction and Critical Angle

This question involves the concept of refraction and critical angle in optics. The figure shows two light rays entering a medium (likely from air to a denser medium) at different angles. The angles θ₁ and θ₂ are the angles of incidence, and x and y are the angles of refraction. The critical angle is the angle of incidence for which the angle of refraction is 90°.

Step-by-Step Reasoning:

Step 1: Understand the relationship between angle of incidence and angle of refraction using Snell's Law. Snell's Law states:

$n1\sin \left(\theta i\right)=n2\sin \left(\theta r\right)$

where n₁ and n₂ are the refractive indices of the two media, θᵢ is the angle of incidence, and θᵣ is the angle of refraction.

Step 2: For a ray going from air (n₁ ≈ 1) to a denser medium (n₂ > 1), sin(θᵣ) = (n₁/n₂) sin(θᵢ). Since n₁/n₂ < 1, θᵣ < θᵢ. So, the refracted ray bends towards the normal.

Step 3: The critical angle (θ_c) is given by:

$\sin \left(\theta c\right)=\frac{n}{2}/n1$ (when n₂ < n₁, for total internal reflection).

In this case, since the ray is entering a denser medium, critical angle is not directly applicable for refraction, but it is important for understanding the limits.

Step 4: In the figure, one ray has a larger angle of incidence (θ₂) and is refracted at 90°, meaning it is at the critical angle. So, θ₂ = θ_c. The other ray has a smaller angle of incidence (θ₁) and refracts at an angle x < 90°.

Step 5: Since θ₂ is the critical angle and θ₁ < θ₂, we have θ₂ > θ₁. Also, for θ₁, the refraction angle x is less than 90°, and for θ₂, y = 90°. So, x < y.

Final Answer: The correct options are θ₂ > θ₁ and y > x.

Related Topics:

• Snell's Law
• Critical Angle
• Total Internal Reflection
• Refractive Index

Formulae and Theory:

Snell's Law: $n1\sin \left(\theta 1\right)=n2\sin \left(\theta 2\right)$

Critical Angle: $\theta c={\sin }^{-1}\left(\frac{n}{2}/n1\right)$, for n₁ > n₂

Refraction: When light passes from one medium to another, it bends due to change in speed. The bending is towards the normal when entering a denser medium.