Reflection — Set 7

Correct Answer: D. Positive and less than 1

• **Positive and less than 1** = A convex mirror always forms a virtual, erect, diminished image; erect means m > 0 (positive), and diminished means |m| < 1. • **0 < m < 1** — regardless of object position, the convex mirror image is always smaller than the object, giving magnification strictly between 0 and +1. • 💡 Wrong-option analysis: Negative and greater than 1: negative m means inverted image; convex mirrors always form erect images; Negative and less than 1: again, negative m implies an inverted image which convex mirrors never produce; Positive and greater than 1: m > 1 would mean the image is magnified; convex mirrors always produce diminished images.

Correct Answer: C. No unit (dimensionless)

• **No unit (dimensionless)** = Reflectance is the ratio of reflected power to incident power; since both have units of watts, the ratio is dimensionless. • **R = P_reflected / P_incident** — as a dimensionless ratio it ranges from 0 (total absorption) to 1 (perfect reflection) and is often expressed as a percentage. • 💡 Wrong-option analysis: Watt: watts measure power (energy per unit time); reflectance is a ratio of powers and is therefore unitless; Meter: metres measure length and are entirely unrelated to reflectance; Candela: candela is the SI unit of luminous intensity; it is related to perceived brightness, not to the power ratio that defines reflectance.

Correct Answer: C. Hard and smooth

• **Hard and smooth** = Hard, non-porous surfaces have high acoustic impedance compared to air, causing most sound energy to be reflected rather than absorbed or transmitted. • **Concert hall walls** — plaster, concrete, and stone walls are used to direct and reflect sound; their hardness and smoothness make them highly effective reflectors. • 💡 Wrong-option analysis: Highly absorbent: highly absorbent surfaces convert sound to heat and are used to reduce echoes, not to reflect sound; Very thin and flexible: thin, flexible panels vibrate and transmit sound rather than reflecting it efficiently; Soft and porous: soft porous materials (foam, carpets) trap sound in their pores and are used for sound absorption, not reflection.

Correct Answer: C. Above 20 kHz

• **Above 20 kHz** = Ultrasound refers to sound waves with frequencies above 20 kHz, which is the upper limit of normal human hearing; typical SONAR and medical imaging use 1–15 MHz. • **Short wavelength advantage** — higher frequency means shorter wavelength, which can resolve smaller objects and reflects better from small structures, making it ideal for detection. • 💡 Wrong-option analysis: Exactly 50 Hz: 50 Hz is the power grid frequency; sound at 50 Hz is well within the audible range and is not ultrasound; Below 20 Hz: below 20 Hz is the infrasound range, used by elephants and whales for communication, not for echo detection; Between 20 Hz and 200 Hz: this is the low-frequency audible range (bass sounds), not ultrasound.

Correct Answer: A. 34 m

• **34 m** = d = v × t / 2 = 340 × 0.2 / 2 = 34 m; the factor of 2 accounts for the round trip of sound to the wall and back. • **Round trip** — 0.2 s is the total travel time to the wall and back; the wall is at half the total distance covered. • 💡 Wrong-option analysis: 68 m: this is d = v × t = 340 × 0.2 = 68 m, forgetting to divide by 2 for the return journey; 17 m: this is d = v × t / 4, an incorrect quartering of the distance; 340 m: this is the speed value and has no bearing on the distance for t = 0.2 s.

Correct Answer: D. One millionth of its initial value

• **One millionth of its initial value** = Reverberation time (RT60) is the time for sound intensity to drop by 60 dB; a 60 dB reduction means intensity falls to 10⁻⁶ times (one millionth) of its original value. • **60 dB = 10⁶ reduction** — since dB = 10 log₁₀(I/I₀), a drop of 60 dB means I/I₀ = 10⁻⁶, i.e., one millionth remains. • 💡 Wrong-option analysis: Half of its initial value: a drop to half intensity is only a 3 dB reduction, much less than the 60 dB defining RT60; One tenth of its initial value: one tenth intensity is a 10 dB drop, still far short of the 60 dB standard; Exactly zero instantly: reaching absolute zero intensity is impossible due to background noise; RT60 uses the practical 60 dB threshold.

Correct Answer: D. Foam or thick carpeting

• **Foam or thick carpeting** = Soft, porous materials trap air in their voids; as sound waves enter, energy is converted to heat by viscous friction in the tiny air channels. • **High absorption coefficient** — open-cell foam and thick carpet have absorption coefficients of 0.6–0.9, much higher than glass (0.05) or granite (0.01). • 💡 Wrong-option analysis: Glass panel: glass is hard and non-porous with a low absorption coefficient (~0.05); it reflects most sound and is a poor absorber; Polished granite: granite is extremely hard and smooth, giving it a very low absorption coefficient (~0.01); it is one of the best sound reflectors; Steel sheet: steel is a hard metal that reflects sound efficiently; its absorption coefficient is near zero.

Correct Answer: A. Infinite

• **Infinite** = A plane mirror has zero curvature, so its radius of curvature R = ∞; since f = R/2, the focal length is also infinite. • **Parallel reflected rays** — an infinite focal length means parallel incident rays remain parallel after reflection; a plane mirror neither converges nor diverges light. • 💡 Wrong-option analysis: Equal to its thickness: the thickness of the glass backing has no relevance to the optical focal length of the reflecting surface; Zero: f = 0 would correspond to infinite curvature (a point-like mirror), which is physically meaningless; Half of its length: the length (aperture) of the mirror is a geometric dimension unrelated to its focal length.

Correct Answer: C. Beyond the center of curvature

• **Beyond the center of curvature** = When u > 2f, the mirror formula gives f < v < 2f; since |v| < |u|, the magnification |m| = |v/u| < 1, meaning the real image is diminished. • **Object beyond 2f** — object between f and 2f gives magnified real image; at 2f gives same-size; beyond 2f gives diminished real image. • 💡 Wrong-option analysis: At the focus: an object at the focus produces reflected parallel rays — the image is at infinity, not diminished; Between pole and focus: this gives a virtual, erect, magnified image, not a diminished real one; At the center of curvature: at u = 2f, the image is also at 2f with m = −1 (same size), not diminished.

Correct Answer: B. Virtual and erect

• **Virtual and erect** = A plane mirror forms a virtual image because reflected rays diverge and only appear to meet behind the mirror; the image is erect (same orientation as object) and the same size. • **m = +1, behind mirror** = The image is behind the mirror at the same distance as the object, virtual (cannot be projected on a screen), and upright. • 💡 Wrong-option analysis: Virtual and inverted: a virtual image from a plane mirror is always erect, not inverted; inverted virtual images cannot be formed by a plane mirror; Real and erect: real images from mirrors are always inverted; an erect real image cannot be formed by any single standard mirror; Real and inverted: plane mirrors never produce real images; real images require actual convergence of reflected rays in front of the mirror.