Light – Reflection and Refraction

Overview

Light is one of the most scoring topics in Railway Group D General Science, typically yielding 2–4 questions per paper. The topic covers fundamental optical phenomena that students observe daily—mirrors, lenses, rainbows, and vision—making it both relatable and testable. Mastery requires understanding how light behaves at surfaces (reflection) and boundaries (refraction), plus the practical applications in optical instruments and the human eye.

Railway exams focus on direct formula application, conceptual identification (concave vs convex properties), and real-world devices (periscope, microscope, spectacles). You must memorize sign conventions, basic ray diagrams, and numerical problem-solving for mirror and lens formulas. Questions range from theoretical ("Which mirror is used in vehicle headlights?") to numerical ("Find image distance given object distance and focal length"). Dispersion and the human eye are typically asked as 1–2 recall-based questions.

The key to scoring is: learn the mirror/lens formula cold, remember the practical uses of each optical element, and understand the single-line explanations of phenomena like myopia correction or rainbow formation.

Key Concepts

• **Reflection of Light**: Light bounces off surfaces following two laws—(i) incident ray, reflected ray and normal lie in one plane; (ii) angle of incidence equals angle of reflection. Plane mirrors form virtual, erect, laterally inverted images at the same distance behind the mirror.
• **Spherical Mirrors**: Concave mirrors converge light (focus is real, in front); convex mirrors diverge light (focus is virtual, behind). Focal length f = R/2 where R is radius of curvature. Concave mirrors can form real or virtual images depending on object position; convex mirrors always form virtual, diminished, erect images.
• **Refraction of Light**: Light bends when passing from one medium to another due to speed change. If entering a denser medium, it bends toward the normal; entering a rarer medium, it bends away. Refractive index n = speed of light in vacuum / speed in medium.
• **Lenses**: Convex (converging) lenses bring parallel rays to a real focus; concave (diverging) lenses spread rays from a virtual focus. Power of lens P (in dioptre) = 1/f (in metres). Convex lenses form real inverted images when object is beyond focal length, virtual magnified when within; concave lenses always form virtual, erect, diminished images.
• **Prism and Dispersion**: White light splits into seven colours (VIBGYOR) when passing through a prism because different wavelengths refract differently (violet bends most, red least). This is dispersion. Rainbows form by dispersion and internal reflection in water droplets.
• **Human Eye**: The eye lens is convex and flexible; ciliary muscles adjust its curvature (accommodation) to focus near or far objects on the retina. The retina contains rods (dim light, black-white vision) and cones (bright light, colour vision).
• **Defects of Vision**: Myopia (short-sightedness)—distant objects blurry, corrected by concave lens. Hypermetropia (long-sightedness)—near objects blurry, corrected by convex lens. Presbyopia—age-related loss of accommodation, corrected by bifocal lenses.
• **Total Internal Reflection**: When light travels from denser to rarer medium at angle greater than critical angle, it reflects completely back into denser medium. Used in optical fibres and sparkling of diamonds.

Formulas / Key Facts

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

**Magnification (Mirrors)**: m = -v/u = height of image / height of object

**Lens Formula**: 1/f = 1/v - 1/u (same symbols as mirror)

**Magnification (Lenses)**: m = v/u = height of image / height of object

**Power of Lens**: P = 1/f (f in metres; P in dioptres D)

**Refractive Index**: n = c/v (c = speed in vacuum ≈ 3×10⁸ m/s, v = speed in medium)

**Snell's Law**: n₁ sin i = n₂ sin r (i = angle of incidence, r = angle of refraction)

**Sign Convention (New Cartesian)**: Distances measured from pole/optical centre; left is negative, right is positive; heights above principal axis positive, below negative.

**Critical Angle**: sin C = 1/n (for denser to rarer medium; n = refractive index of denser medium)

**Focal length concave mirror/convex lens**: Positive (real focus). Focal length convex mirror/concave lens: Negative (virtual focus).

Worked Examples

**Example 1**: An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Find the image distance and magnification.

*Solution*: Given: u = -30 cm (object is on left, negative), f = -20 cm (concave mirror, negative) Using 1/f = 1/v + 1/u: 1/(-20) = 1/v + 1/(-30) 1/v = -1/20 + 1/30 = (-3 + 2)/60 = -1/60 v = -60 cm Magnification m = -v/u = -(-60)/(-30) = -2 **Answer**: Image distance 60 cm in front of mirror (real image), magnification -2 (inverted, magnified twice).

**Example 2**: A convex lens has power +2 D. What is its focal length?

*Solution*: P = 1/f 2 = 1/f f = 1/2 = 0.5 m = 50 cm **Answer**: Focal length is 50 cm or +0.5 m.

**Example 3**: Light travels from air (n=1) to glass (n=1.5) at 30° incidence. Find angle of refraction.

*Solution*: Snell's law: n₁ sin i = n₂ sin r 1 × sin 30° = 1.5 × sin r 0.5 = 1.5 sin r sin r = 0.5/1.5 = 1/3 ≈ 0.333 r ≈ 19.5° **Answer**: Angle of refraction approximately 19.5° (light bends toward normal in denser medium).

Common Mistakes

**Sign Convention Errors → Always apply New Cartesian sign convention**: Treat distances toward incident light as negative (object side) and away as positive (image side). Many students mix up signs for u, v, f leading to wrong answers. *Fix*: Memorize "left is minus, right is plus" and stick to it rigidly.

**Confusing Mirror and Lens Formulas → Mirror uses 1/f = 1/v + 1/u; Lens uses 1/f = 1/v - 1/u**: Students often write addition for both. *Fix*: Remember "mirror adds, lens subtracts" in the formula.

**Forgetting Power = 1/f requires f in metres**: Students use f in cm and get wrong power. *Fix*: Always convert focal length to metres before calculating power. If f = 25 cm, use f = 0.25 m, so P = 4 D.

**Mixing up concave/convex properties**: Students say "concave lens converges" or "convex mirror is used in headlights." *Fix*: Concave = Converging for mirrors, Diverging for lenses. Convex = Diverging for mirrors, Converging for lenses. Use mnemonic "MirrorC² = Mirror Concave Converges."

**Assuming virtual image means no image formation**: Virtual images are real perceptions formed by extended reflected/refracted rays; they cannot be projected on screen but are visible to eye. *Fix*: Understand virtual = "appears to be at a location" and can be seen directly by observer.

Quick Reference

• **Concave mirror**: Converging, real/virtual images, used in torches, shaving mirrors, solar cookers.
• **Convex mirror**: Diverging, always virtual/erect/diminished, used in vehicle rear-view mirrors for wide field.
• **Concave lens**: Diverging, always virtual/erect/diminished, corrects myopia (short sight).
• **Convex lens**: Converging, real/virtual images, used in cameras, magnifying glasses; corrects hypermetropia (long sight).
• **Prism**: Disperses white light into VIBGYOR; violet deviates most, red least.
• **Human eye defects**: Myopia (concave lens), Hypermetropia (convex lens), Presbyopia (bifocal).
• **Sign convention**: Object distance u always negative, real image v positive, virtual image v negative; concave mirror/convex lens f negative, convex mirror/concave lens f positive—**wait, correction**: concave mirror and convex lens have f *negative* and *positive* respectively under New Cartesian (concave mirror f is negative, convex lens f is positive).
• **Power formula**: P(D) = 1/f(m); combination of lenses: P_total = P₁ + P₂.
• **Critical angle**: Light passes denser to rarer; if angle > critical angle, total internal reflection occurs (optical fibres).