Skip to content

Grade 10th · Physics · Light - Reflection and Refraction

Snell's Law of Refraction: Formula, Derivation & Solved Examples — Class 10 Physics

Master Snell's Law of Refraction (n = sin i / sin r) for Class 10 Physics. Complete step-by-step derivation, refractive index formula, lateral displacement, and NCERT solved numerical problems.

Science StreamFundamental Level

Advertisement

⚡

Essential Formulas & Mathematical Definitions

n₂₁ = sin(i) / sin(r)
n = c / v (Absolute Refractive Index)
n₂₁ = n₂ / n₁ = v₁ / v₂
sin(C) = 1 / n (Critical Angle)

Statement of Snell's Law of Refraction

The second law of refraction, discovered by Willebrord Snell in 1621, states: The ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is a constant for light of a given color and for a given pair of media. Mathematically: sin(i) / sin(r) = constant = n₂₁, where n₂₁ is the refractive index of the second medium with respect to the first medium.

Step-by-Step Derivation & Physical Meaning

When a light ray travels from Medium 1 (speed v₁) to Medium 2 (speed v₂), the wavefront bends due to the change in phase velocity. From wave kinematics: sin(i) / sin(r) = v₁ / v₂. Since absolute refractive index is defined as n = c / v, we have v₁ = c / n₁ and v₂ = c / n₂. Substituting these yields: sin(i) / sin(r) = (c / n₁) / (c / n₂) = n₂ / n₁ = n₂₁. Therefore: n₁ × sin(i) = n₂ × sin(r).

Rules of Bending: Rarer to Denser vs Denser to Rarer

Case 1: Light travels from an optically rarer medium to an optically denser medium (e.g., air to glass, n₂ > n₁). The ray bends towards the normal (r < i). Case 2: Light travels from an optically denser medium to an optically rarer medium (e.g., glass to air, n₂ < n₁). The ray bends away from the normal (r > i).

Refraction Through a Glass Slab & Lateral Shift

When a ray enters a rectangular glass slab at angle i and exits into air, the emergent ray is parallel to the incident ray (i = e). However, it is laterally displaced by distance d = t × sin(i - r) / cos(r), where t is the slab thickness.

📋

Exam Day Revision & Problem Solving Checklist

  • ✓State Snell's law verbatim for 2-mark CBSE board questions
  • ✓Ensure angles of incidence (i) and refraction (r) are measured from the NORMAL, not the surface interface
  • ✓Use n = c / v with c = 3 × 10⁸ m/s for absolute refractive index numericals
  • ✓Verify that relative refractive index n₂₁ is reciprocal to n₁₂ (n₂₁ = 1 / n₁₂)
🎯

High-Yield Exam Strategy & Scoring Tips

Step-by-Step Mark Allocation

Always state the governing principle or formula first, write given values with standard SI units, substitute clearly, and highlight the final numerical answer with units in a box for full step marking.

Common Calculation Traps

Watch for unit prefixes (cm to m, minutes to seconds, g to kg, degrees to radians). In coordinate and ray optics problems, double-check Cartesian sign conventions before computing.

Recommended Practice & Calculation Tools

Test your understanding and perform instant calculations with these free online utilities.

Scientific Physics Motion & Electricity Calculator

Solve core physics formulas for Grade 10th, 11th, and 12th: motion kinematics, force, Ohm's law, and wave physics.

Open Tool

Percentage Calculator

Find percentages, percentage change, and what percent one number is of another.

Open Tool

Frequently Asked Exam Questions & Concept Clarifications

What is Snell's law in Class 10 Physics?

Snell's law states that for a given pair of media and color of light, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant: sin(i) / sin(r) = n₂₁ (refractive index).

What is the unit of refractive index?

Refractive index is a dimensionless pure ratio of two similar quantities (either ratio of sines of angles or ratio of velocities: c/v), so it has NO units.

Why does a pencil appear bent in a glass of water?

Light rays coming from the submerged portion of the pencil travel from water (optically denser) to air (optically rarer), bending away from the normal. To the observer, the rays appear to come from an apparent shallower position, creating the illusion of a bend at the water surface.