Reflection — Set 3

Correct Answer: A. Normal

• **Normal** = By convention, all reflection angles (angle of incidence and angle of reflection) are measured from the normal — a line perpendicular to the reflecting surface at the point of incidence. • **90° complement** — the angle a ray makes with the surface equals 90° minus its angle with the normal; measuring from the normal keeps angles small and symmetric. • 💡 Wrong-option analysis: Mirror surface: measuring from the surface gives the grazing angle, which is the complement of the incidence angle; this convention is not used in standard optics; Direction of motion of the object: the object's motion direction is irrelevant to defining reflection angles; Principal axis only: the principal axis is a specific line for spherical mirrors and is unrelated to the general definition of reflection angles.

Correct Answer: B. 24 cm

• **24 cm** = Using mirror formula 1/f = 1/v + 1/u with f = −12 cm and u = −24 cm: 1/v = 1/f − 1/u = −1/12 + 1/24 = −1/24, so v = −24 cm (real image, 24 cm in front). • **Object at 2f → image at 2f** — when the object is at the centre of curvature (u = 2f), the image also forms at the centre of curvature, real, inverted, and same size. • 💡 Wrong-option analysis: 12 cm: this would be v = f, which occurs when the object is at infinity, not at 2f; 48 cm: this would correspond to an object between f and 2f producing a magnified real image; 18 cm: this image distance has no correspondence to the given object and focal length with the mirror formula.

Correct Answer: A. +1

• **+1** = A plane mirror forms an image of the same size as the object; since the image is virtual and erect, the magnification m = +1. • **m = −v/u = −(−20)/(−20) = +1** — applying the formula confirms the image is the same size and erect (positive sign). • 💡 Wrong-option analysis: 0: zero magnification would mean no image, which is impossible; −1: negative magnification would mean the image is inverted, but plane mirror images are always erect; Greater than 1: magnification > 1 means enlarged image, which is only possible for objects within the focal length of a concave mirror, not for plane mirrors.

Correct Answer: B. At the center of curvature, real, inverted, and same size

• **At the center of curvature, real, inverted, and same size** = When u = R = 2f, mirror formula gives v = 2f; magnification m = −v/u = −1, confirming same size and inverted. • **m = −1** — a magnification of −1 means the image is real, inverted, and exactly the same size as the object; it forms at the same position as the object. • 💡 Wrong-option analysis: Behind the mirror, virtual and magnified: virtual magnified images require the object to be within the focal length; At the focus, real and diminished: the focus position corresponds to an object at infinity, not at 2f; At infinity: an image at infinity corresponds to an object at the focus, not at the centre of curvature.

Correct Answer: C. Kaleidoscope

• **Kaleidoscope** = A kaleidoscope contains two or three plane mirrors inclined at an angle; multiple reflections between them create a set of symmetrical colourful patterns. • **n = 360°/θ − 1 images** — for mirrors at angle θ, the number of images formed is (360/θ) − 1; at 60° this gives 5 images arranged symmetrically. • 💡 Wrong-option analysis: Spectrometer: a spectrometer uses a prism or diffraction grating to measure wavelengths of light, not to create decorative patterns; Telescope: a telescope collects and magnifies distant objects using lenses or curved mirrors, unrelated to multiple reflections for patterns; Microscope: a microscope magnifies small nearby objects using lenses, not multiple mirror reflections.

Correct Answer: C. Magnified upright image for close objects

• **Magnified upright image for close objects** = When an object (tooth) is placed within the focal length of a concave mirror, the image is virtual, erect, and magnified, making fine details visible. • **Object inside focal length** — this is the same principle used in shaving/makeup mirrors; the face must be held closer than the focal length to see a magnified erect image. • 💡 Wrong-option analysis: Virtual image only of smaller size: convex mirrors produce smaller virtual images; concave mirrors produce magnified virtual images for close objects; Diminished real image: diminished real images require the object beyond 2f and are not useful for dental examination; Same-size image at all positions: only a plane mirror produces m = +1 at all object positions; a concave mirror's magnification varies with object distance.

Correct Answer: D. 20°

• **20°** = When a plane mirror rotates by angle α, the normal rotates by α, both the incidence and reflection angles change by α, so the reflected ray rotates by 2α = 2 × 10° = 20°. • **Rotation law of mirrors** — the factor of 2 arises because both the angle of incidence and the angle of reflection change when the mirror tilts; this principle is used in galvanometers. • 💡 Wrong-option analysis: 15°: 1.5 times the mirror rotation has no physical basis; 10°: this equals the mirror rotation angle itself and ignores the doubling effect; 5°: this is half the mirror rotation and is incorrect; the law states the reflected ray rotates by twice the mirror's rotation.

Correct Answer: D. Behind the mirror and virtual

• **Behind the mirror and virtual** = A convex mirror diverges parallel rays after reflection; when extended backward, they appear to meet at a point behind the mirror called the virtual focus. • **f is positive in some conventions** — because the focus is virtual (behind the mirror), it is considered positive in the new Cartesian convention for a convex mirror. • 💡 Wrong-option analysis: At the pole only: the pole is just the centre of the mirror surface; the focus is at distance f = R/2 from the pole; In front of the mirror and real: a real focus in front of the mirror describes a concave mirror, not convex; At the center of curvature only: the centre of curvature is at distance R behind the mirror, different from the focus at R/2.

Correct Answer: A. Persistence of sound due to multiple reflections

• **Persistence of sound due to multiple reflections** = Reverberation is the prolonged presence of sound in an enclosed space after the source stops, caused by repeated reflections off walls, ceiling, and floor. • **RT60** — reverberation time is defined as the time for sound intensity to drop by 60 dB (one millionth of the original); it governs the acoustic character of halls and theatres. • 💡 Wrong-option analysis: Bending of sound around obstacles: this describes diffraction of sound, not reverberation; Change of sound frequency due to motion: this describes the Doppler effect, which involves moving sources or observers, not reflections; Complete absence of sound: complete absence is called silence or anechoic condition; reverberation is the opposite — prolonged presence of sound.

Correct Answer: A. Reflect sound toward the audience evenly

• **Reflect sound toward the audience evenly** = Curved reflectors above the stage focus and direct sound energy uniformly toward the seated audience, improving loudness and clarity. • **Concave reflector geometry** — a concave reflector placed above a speaker can direct sound downward just as a concave mirror focusses light, without changing its frequency. • 💡 Wrong-option analysis: Block sound completely: blocking sound is the purpose of acoustic barriers and soundproofing materials, not reflectors; Increase frequency of sound: frequency of sound is determined by the source and remains unchanged by reflection; Absorb all sound: sound absorption is achieved by soft, porous materials; reflectors are hard surfaces designed to reflect, not absorb.