8.3 Sound & Light

Why Sound and Light Matter for RRB Group D

Sound and light together account for roughly 3–4 of the physics questions in the General Science section. RRB frequently tests the nature of sound waves, echoes, SONAR, the laws of reflection and refraction, the mirror and lens formulas, and the defects of the human eye and their corrections.

Sound

Sound is a longitudinal mechanical wave produced by vibrating bodies. It needs a material medium (solid, liquid, or gas) and cannot travel through vacuum — this is why sound from an explosion in space would not be heard.

Key Properties

v = f λ

Speed of Sound in Different Media

Speed of sound increases with temperature in air (≈ 0.6 m/s per °C) and is higher in solids than in liquids, and higher in liquids than in gases, because of closer particle spacing.

Echo and Reverberation

An echo is the reflected sound heard after the original sound. For a distinct echo the reflecting surface must be at least 17 m away from the listener (since the human ear can distinguish sounds separated by about 0.1 s, and 2 × 17 / 343 ≈ 0.1 s).

Reverberation is the persistence of sound due to repeated reflections. Auditoriums use sound-absorbing materials on walls to reduce reverberation time.

SONAR and Ultrasound

SONAR (Sound Navigation And Ranging) uses ultrasonic waves to measure the depth of the sea bed or to locate submarines. The depth d = v × t / 2, where t is the time for the wave to travel to the sea bed and back.

Ultrasound (frequency > 20,000 Hz) is used in medical imaging, detecting flaws in metal blocks, and cleaning parts where ordinary cleaning is difficult.

The Human Ear

Sound waves enter through the outer ear, vibrate the ear drum (tympanic membrane), and the vibrations are transmitted by the three tiny bones (hammer, anvil, stirrup) of the middle ear to the inner ear (cochlea), which converts them to electrical signals carried by the auditory nerve to the brain.

Light

Light is a transverse electromagnetic wave that can travel through vacuum at c ≈ 3 × 10⁸ m/s. It exhibits reflection, refraction, dispersion, and interference.

Reflection and the Mirror Formula

Laws of reflection: (1) the incident ray, the reflected ray, and the normal all lie in the same plane; (2) the angle of incidence equals the angle of reflection.

Mirror formula: 1/v + 1/u = 1/f

Sign convention (New Cartesian, as used in NCERT): the pole is the origin, the principal axis is the x-axis, and light is taken to travel from left to right. Distances measured along the direction of the incident light (to the right of the pole) are positive; distances measured against it (to the left) are negative. Two consequences you will use in every mirror question: the object always sits to the left, so u is always negative; and the focus of a concave mirror lies in front of the mirror (to the left), so f is negative, while the focus of a convex mirror lies behind it, so f is positive. Watch the sign trap — a "positive focal length" belongs to the convex mirror, the opposite of the lens case.

Refraction and Snell's Law

When light passes from one transparent medium to another, it bends. Snell's law: n₁ sin i = n₂ sin r, where n is the refractive index.

Refractive index of water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42.

Lenses and the Lens Formula

A convex (converging) lens is thicker at the centre; a concave (diverging) lens is thinner at the centre.

Lens formula: 1/v − 1/u = 1/f

Magnification: m = v/u = h_i/h_o (image height over object height).

Power of a lens: P = 1 / f (with f in metres); SI unit dioptre (D). A convex lens has positive power, a concave lens negative power.

Worked Example

A convex lens has focal length 20 cm. An object is placed 30 cm in front of it. Find the image distance.

Assign the signs first. For lenses the optical centre is the origin: the object is on the left, so u = −30 cm, and a convex lens has a positive focal length, so f = +20 cm. (Note the contrast with mirrors, where the concave mirror is the one with negative f.)

Substitute into 1/v − 1/u = 1/f:

1/v = 1/f + 1/u = 1/20 + 1/(−30) = (3 − 2)/60 = 1/60.

v = +60 cm. A positive v means the image forms on the far side of the lens, so it is real and inverted. Magnification m = v/u = 60/(−30) = −2, so the image is twice the object's size and inverted — consistent with an object placed between f and 2f.

The Human Eye and Its Defects

The human eye forms an image on the retina using the cornea and the eye lens. The iris controls the size of the pupil, which regulates the amount of light entering.

The least distance of distinct vision (near point) for a normal adult eye is 25 cm. The far point of a normal eye is at infinity.

Dispersion and Prism

White light passing through a prism splits into seven colours (VIBGYOR: violet, indigo, blue, green, yellow, orange, red) — the phenomenon of dispersion. Violet deviates the most, red the least, because refractive index is highest for violet and lowest for red. A rainbow is a natural spectrum formed by dispersion of sunlight through raindrops.