Reflection — Set 1

Correct Answer: A. 20 cm behind the mirror

• **20 cm behind the mirror** = A plane mirror always forms the image at the same perpendicular distance behind the mirror as the object is in front. • **Image distance = Object distance** — for a plane mirror, if u = 20 cm in front, then v = 20 cm behind, making the total object-to-image distance 40 cm. • 💡 Wrong-option analysis: 40 cm behind the mirror: this is the total object-to-image separation, not the image distance from the mirror; 10 cm behind the mirror: halving the object distance has no basis in plane mirror optics; 20 cm in front of the mirror: the image in a plane mirror is always virtual and behind the mirror, never in front.

Correct Answer: D. The incident ray, reflected ray, and the normal lie in the same plane

• **The incident ray, reflected ray, and the normal lie in the same plane** = The second law of reflection states that these three are always coplanar at the point of incidence. • **Coplanar condition** — this means reflection is a two-dimensional process in the plane of incidence; the reflected ray cannot go out of that plane. • 💡 Wrong-option analysis: The normal always bisects the angle between the rays: the normal does not bisect the angle between incident and reflected rays but lies between them; The angle of incidence equals the angle of reflection: this is the first law of reflection, not the second; The reflected ray is always parallel to the incident ray: parallel rays would imply zero deviation, which only occurs for normal incidence.

Correct Answer: C. 30 cm

• **30 cm** = For any spherical mirror, the radius of curvature R equals twice the focal length: R = 2f. • **R = 2 × 15 cm = 30 cm** — the centre of curvature is always twice as far from the pole as the principal focus. • 💡 Wrong-option analysis: 7.5 cm: this is half the focal length, obtained by dividing instead of multiplying; 45 cm: this is 3f, which has no standard geometric meaning for spherical mirrors; 15 cm: this equals f itself; the radius and focal length are equal only if f = R, which is not the case for spherical mirrors.

Correct Answer: A. 0.1 s

• **0.1 s** = The human ear requires a gap of at least 0.1 s between two sounds to distinguish them separately; a reflected sound arriving sooner merges with the original. • **Persistence of hearing = 0.1 s** — at a speed of sound of 340 m/s, this implies the reflecting wall must be at least 17 m away for a distinct echo. • 💡 Wrong-option analysis: 0.01 s: this is ten times too short; sounds 0.01 s apart are perceived as a single continuous sound; 0.08 s: this is below the 0.1 s threshold and would not produce a distinct separate echo; 0.05 s: this is also below the threshold, causing the reflected sound to blend with the original.

Correct Answer: D. Virtual, erect, and diminished behind the mirror

• **Virtual, erect, and diminished behind the mirror** = A convex mirror diverges reflected rays so they appear to originate from behind the mirror, giving a virtual, upright, and smaller image. • **Always between pole and focus** — the image in a convex mirror always forms between the pole and the virtual focus, regardless of object position. • 💡 Wrong-option analysis: Real, erect, and same size as the object: convex mirrors cannot form real images since reflected rays always diverge; Real, inverted, and enlarged in front of the mirror: inverted real images are formed only by concave mirrors for objects beyond the focus; Virtual, inverted, and enlarged behind the mirror: a virtual image in a convex mirror is always erect and diminished, not inverted or enlarged.

Correct Answer: B. 45°

• **45°** = A plane mirror tilted at 45° to the vertical turns a horizontal light beam through exactly 90° by reflection, redirecting it vertically. • **Two 45° mirrors** — in a periscope the two mirrors are parallel to each other and each at 45°; together they shift the line of sight vertically without rotating the image. • 💡 Wrong-option analysis: 90°: a mirror at 90° to the surface is perpendicular to the light path and would reflect light straight back; 60°: a 60° tilt would deflect light by 120°, not 90°; 30°: a 30° tilt would deflect light by only 60°, making it unusable for the standard 90° deflection in a periscope.

Correct Answer: D. -10 D

• **−10 D** = Mirror power P = 1/f (f in metres); with Cartesian convention a concave mirror has f = −0.10 m, giving P = 1/(−0.10) = −10 D. • **Negative power** — in the Cartesian sign convention a concave mirror has negative focal length, so its power is negative despite being converging. • 💡 Wrong-option analysis: −5 D: this would correspond to f = −0.20 m (20 cm), not 10 cm; +5 D: positive power with f = +0.20 m describes a convex mirror of focal length 20 cm; +10 D: positive power would correspond to a convex mirror, and the magnitude 10 D would require f = 0.10 m in magnitude.

Correct Answer: D. Lateral inversion

• **Lateral inversion** = In a plane mirror the image appears reversed sideways relative to the object because the mirror reflects front-to-back, which our brain interprets as left-right reversal. • **Front-to-back reversal** — technically the mirror reverses the depth axis (front-back), but since humans are bilaterally symmetric we perceive it as left-right swap. • 💡 Wrong-option analysis: Rotation: rotation would mean the image is turned by some angle, not simply mirrored; Refraction: refraction is the bending of light at a boundary between two media and is unrelated to image reversal in mirrors; Dispersion: dispersion is the splitting of white light into its component colours and has nothing to do with image orientation.

Correct Answer: D. Reflected light energy to incident light energy

• **Reflected light energy to incident light energy** = Reflectance (R) is the fraction of incident radiant energy that is reflected, defined as R = Reflected power / Incident power. • **Dimensionless, 0 to 1** — a perfect reflector has R = 1 (100%) and a perfect absorber has R = 0; real surfaces have values between these limits. • 💡 Wrong-option analysis: Transmitted light energy to absorbed light energy: this ratio has no standard optical name and does not describe reflectance; Absorbed light energy to reflected light energy: this is the ratio of absorbed to reflected energy, which has no standard name and is the inverse of what is useful; Incident light energy to reflected light energy: inverting the ratio gives 1/R (the reciprocal of reflectance), not reflectance itself.

Correct Answer: B. 0°

• **0°** = All reflection angles are measured from the normal; a ray incident along the normal makes 0° with it, so by the first law of reflection the angle of reflection is also 0°. • **Retroreflection** — the ray reflects straight back along its original path; this is why a laser aimed perpendicularly at a mirror returns to its source. • 💡 Wrong-option analysis: 90°: 90° is the angle the incident ray makes with the mirror surface, not with the normal; 45°: 45° is the incidence angle for a mirror set at 45°, not for normal incidence; It depends on the mirror material: the laws of reflection apply to all smooth reflecting surfaces regardless of material.