Study Notes: Light — Reflection and Refraction (Class 10)

Overview

Light — Reflection and Refraction is one of the highest-weightage topics in NSO Class 10 Science. It combines conceptual understanding with numerical problem-solving, covering both mirrors and lenses. Students must master sign conventions, formula application, and the behavior of light at boundaries between different media.

This topic typically yields 3–5 questions in NSO, mixing formula-based calculations (focal length, magnification, power) with conceptual questions (ray diagrams, image characteristics, real-life applications). The Achievers Section often tests this topic through multi-step problems involving combinations of optical devices or tricky sign convention scenarios.

Strong command over sign conventions and quick recall of mirror/lens formulas is essential. Practice drawing accurate ray diagrams and solving numerical problems under time pressure to excel.

Key Concepts

• **Laws of Reflection**: The incident ray, reflected ray, and normal all lie in the same plane. The angle of incidence equals the angle of reflection (∠i = ∠r).

• **Spherical Mirrors**: Concave mirrors converge light (can form real or virtual images), while convex mirrors diverge light (always form virtual, diminished, erect images). The principal focus of a concave mirror is real; for a convex mirror, it is virtual.

• **Refraction**: When light travels from one transparent medium to another, it changes speed and bends at the boundary. Light bends toward the normal when entering a denser medium and away when entering a rarer medium.

• **Refractive Index**: The refractive index n of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium. n = c/v. Higher refractive index means light travels slower in that medium.

• **Snell's Law**: At the interface of two media, n₁ sin i = n₂ sin r, where n₁ and n₂ are refractive indices and i, r are angles of incidence and refraction.

• **Total Internal Reflection**: When light travels from denser to rarer medium and the angle of incidence exceeds the critical angle, light reflects entirely back into the denser medium. This principle underlies optical fibers and phenomena like mirages.

• **Lenses**: Convex lenses converge light (real focus, can form real or virtual images), while concave lenses diverge light (virtual focus, always form virtual, diminished, erect images). Lens behavior depends on the curvature and refractive index.

• **Power of Lens**: Power P = 1/f (in meters). Measured in diopters (D). Positive for convex lenses, negative for concave lenses. Power is additive for lenses in contact: P_total = P₁ + P₂.

Formulas / Key Facts

**Mirror Formula**: 1/f = 1/v + 1/u where f = focal length, v = image distance, u = object distance.

**Magnification (mirrors and lenses)**: m = -v/u = h₂/h₁ where h₁ = object height, h₂ = image height. Negative magnification means inverted image.

**Lens Formula**: 1/f = 1/v - 1/u (same as mirror formula in structure, different sign convention application).

**Power of Lens**: P = 1/f (f in meters), measured in diopters (D).

**Refractive Index**: n = c/v = (Real depth)/(Apparent depth) = sin i / sin r.

**Snell's Law**: n₁ sin i = n₂ sin r.

**Sign Convention (New Cartesian)**: Distances measured from the pole/optical center. Along the direction of incident light is positive; opposite is negative. Heights above principal axis are positive; below are negative. Focal length: positive for concave mirrors and convex lenses; negative for convex mirrors and concave lenses.

**Critical Angle**: sin C = n₂/n₁ (when light goes from denser n₁ to rarer n₂). For glass-air, C ≈ 42°; for water-air, C ≈ 49°.

**Lens Maker's Formula**: 1/f = (n-1)(1/R₁ - 1/R₂) where n = refractive index of lens material relative to surroundings, R₁ and R₂ are radii of curvature.

Worked Examples

**Example 1**: A concave mirror has a focal length of 15 cm. An object is placed 30 cm in front of it. Find the image distance and magnification.

*Solution*: Given f = -15 cm (concave mirror), u = -30 cm (object on left side). Using mirror formula: 1/f = 1/v + 1/u 1/(-15) = 1/v + 1/(-30) 1/v = -1/15 + 1/30 = -2/30 + 1/30 = -1/30 v = -30 cm The image is 30 cm in front of the mirror (real, inverted). Magnification m = -v/u = -(-30)/(-30) = -1 Image is same size as object, inverted.

**Example 2**: A convex lens of focal length 20 cm forms an image at 60 cm. Find the object distance and magnification.

*Solution*: Given f = +20 cm (convex lens), v = +60 cm (real image). Using lens formula: 1/f = 1/v - 1/u 1/20 = 1/60 - 1/u 1/u = 1/60 - 1/20 = 1/60 - 3/60 = -2/60 = -1/30 u = -30 cm Object is 30 cm on the left side of the lens. Magnification m = v/u = 60/(-30) = -2 Image is twice the size of object, inverted.

**Example 3**: Light travels from glass (n = 1.5) to air (n = 1.0) at 45° incidence. Will total internal reflection occur?

*Solution*: First find critical angle: sin C = n₂/n₁ = 1.0/1.5 = 0.667 C = sin⁻¹(0.667) ≈ 42° Since angle of incidence (45°) > critical angle (42°), total internal reflection occurs. Light will not emerge into air.

Common Mistakes

**Wrong Sign Convention**: Students often forget that object distance u is always negative in the New Cartesian system. *Fix*: Always place the object on the left; measure all distances from the pole/center with proper signs.

**Confusing Mirror and Lens Formulas**: The mirror formula has 1/f = 1/v + 1/u while lens formula is 1/f = 1/v - 1/u. *Fix*: Memorize lens formula as "v minus u" and apply consistent sign rules.

**Magnification Sign Error**: Treating magnification as always positive. *Fix*: Remember m = -v/u. Negative m means inverted image; positive m means erect image. Also, |m| > 1 means enlarged; |m| < 1 means diminished.

**Mixing Real/Virtual Image Properties**: Assuming virtual images cannot be seen or projected. *Fix*: Real images form where rays actually meet (can be caught on screen); virtual images form where rays appear to come from (cannot be caught but are visible to the eye).

**Refractive Index Inversions**: Using n = v/c instead of n = c/v. *Fix*: Refractive index is always ≥ 1 for any medium compared to vacuum. Speed in medium is less, so n = c/v.

**Power Calculation Error**: Using focal length in cm instead of meters. *Fix*: Convert focal length to meters before calculating power. P = 1/f where f is in meters.

Quick Reference

• **Concave mirror**: f negative, converges light, real/virtual images possible.
• **Convex mirror**: f positive (by magnitude convention), diverges light, always virtual/erect/diminished image.
• **Convex lens**: f positive, converges light, real/virtual images possible.
• **Concave lens**: f negative, diverges light, always virtual/erect/diminished image.
• **Sign rule**: Object distance u always negative; v negative = real image (mirror)/virtual (lens); v positive = virtual (mirror)/real (lens).
• **Power addition**: P_net = P₁ + P₂ for lenses in contact.
• **Total internal reflection**: Possible only when light goes from denser to rarer medium and i > critical angle.