Optics and Sound Questions for NDA

Reflection of Light and Mirrors

When light bounces off a surface, it follows two laws: angle of incidence equals angle of reflection, and both rays and the normal lie in the same plane. Curved mirrors (concave and convex) follow the mirror formula. Concave mirrors converge light and are used in torches, headlights, and shaving mirrors. Convex mirrors diverge light and always form virtual, erect, diminished images — used in rear-view mirrors.

• Concave mirror: center of curvature and focus are in front of mirror (real side)
• Convex mirror: always gives virtual, erect, diminished image regardless of object position
• Focal length f = R/2 where R is radius of curvature
• Sign convention: distances measured from pole; in front of mirror is negative
• Magnification m = -v/u; negative m means inverted image

Refraction and Snells Law

Refraction is bending of light when it travels from one medium to another due to change in speed. The refractive index n of a medium tells how much light slows down compared to vacuum. Denser medium (higher n) bends light toward the normal. This explains why a straw looks bent in water and why a pool looks shallower than it is.

• Refractive index n = speed of light in vacuum / speed in medium = c/v
• Higher n means slower light and more bending
• Apparent depth = Real depth / n (object in denser medium appears shallower)
• Total Internal Reflection (TIR) happens when light goes from denser to rarer medium beyond critical angle
• Critical angle C: sin C = 1/n (for medium to air)
• TIR applications: optical fibre, diamonds, mirages, periscopes

Lenses and Optical Instruments

Convex (converging) lenses are thicker at center; concave (diverging) lenses are thinner at center. Lenses obey the thin lens formula similar to mirrors. Power of a lens in dioptres is the reciprocal of focal length in metres — a key concept for understanding spectacle prescriptions. When lenses are placed in contact, their powers simply add up.

• Convex lens: f is positive, can form real or virtual images depending on object position
• Concave lens: f is always negative, always forms virtual, erect, diminished image
• Power P = 1/f (in metres), unit is dioptre (D)
• Combined power: P = P1 + P2 for lenses in contact
• Human eye defects: Myopia corrected by concave lens; Hypermetropia by convex lens
• Microscope uses two convex lenses; Telescope objective is convex, eyepiece is convex

Sound Waves and Properties

Sound is a longitudinal mechanical wave — it needs a medium to travel and cannot travel through vacuum. Particles vibrate parallel to the direction of wave propagation. Speed of sound in air at 0 degrees C is about 332 m/s and increases with temperature. Sound travels fastest in solids, then liquids, then gases — remember SLG (Solid Liquid Gas, fastest to slowest).

• Sound is longitudinal; light is transverse — key difference
• Speed in air at 0 C = 332 m/s; increases by 0.6 m/s per degree C rise
• Speed order: Solids greater than Liquids greater than Gases
• Frequency below 20 Hz = infrasound; above 20,000 Hz = ultrasound
• Resonance: when forced frequency equals natural frequency, amplitude becomes maximum
• Echo: reflected sound heard after 0.1 second minimum; minimum distance = 17 m from wall

Doppler Effect

The Doppler effect is the apparent change in frequency of sound (or light) when source and observer are in relative motion. If they move toward each other, apparent frequency increases (pitch rises). If they move away, frequency drops. Classic NDA question: a train approaches or moves away — find apparent frequency. Think of it like waves bunching up when source approaches you.

• Source approaching observer: frequency appears higher (wavelength shorter)
• Source moving away: frequency appears lower (wavelength longer)
• Observer moving toward source: frequency increases; moving away: decreases
• Doppler effect in light: blue shift (approaching), red shift (receding) — used in astronomy
• Used in RADAR, SONAR, speed guns, medical ultrasound

• Sign convention errors in mirror and lens formulas: always measure u as negative when object is in front. Forgetting this flips the entire answer.
• Using f = R instead of f = R/2 for mirrors. The focal length is HALF the radius of curvature, not equal to it.
• Confusing concave and convex: students often mix which one converges. Remember Concave = Cave = hollow inward = converges light toward center.
• In Doppler formula, mixing up when to add or subtract velocities. Rule: motion that decreases distance increases frequency — use subtraction in denominator for source approaching.
• Forgetting that echo requires minimum 0.1 second gap between original and reflected sound, and minimum distance of about 17 m. NDA asks this as a conceptual trap.

• SLG for sound speed: Solids beat Liquids beat Gases. Like a soldier marches fastest on solid ground.
• For eye defects: My Convex (Myopia needs Concave lens). Hyper people are Far-sighted (Hypermetropia = Far = Convex lens corrects it).
• CONCAVE = CONverges = CONcentrates light. CONVEX = diVERGes = scatters (remember the X spreads out).
• Doppler: APPROACHING = frequency AMPLIFIES (both start with A). Receding = Reduces frequency (both R words).

• NDA typically asks 1-2 direct numerical questions on mirror or lens formula per paper. Practice plugging in sign convention correctly under time pressure — 30 seconds per question is the target.
• Conceptual questions on TIR, optical fibre, and why convex mirror is used in vehicles appear almost every year. These are easy guaranteed marks if you memorize the one-line reasons.
• Doppler effect questions usually give you a moving train scenario. They test the formula application, not derivation. Know the standard formula and which velocity goes in numerator vs denominator.
• Sound questions often test the boundary: infrasound vs ultrasound frequency limits, applications of ultrasound (SONAR, medical imaging), and echo conditions. These are purely factual and take under 20 seconds.
• In recent NDA papers (2021-2023), optical instruments like microscope magnification and telescope have appeared as single-line conceptual questions. Know which lens is objective and which is eyepiece, and that magnification of microscope is product of both lens magnifications.