Reflection — Set 5

Correct Answer: D. Virtual, erect, and magnified

• **Virtual, erect, and magnified** = When the object is within the focal length, reflected rays diverge after leaving the mirror; extending them backward they appear to meet behind the mirror, giving a virtual, upright, magnified image. • **Magnifying mirror** — this is why a concave mirror is used as a shaving or makeup mirror; the face is held inside the focal length for a magnified erect virtual image. • 💡 Wrong-option analysis: Virtual, inverted, and diminished: a virtual image from a concave mirror is always erect and magnified, never inverted or diminished; Real, erect, and magnified: real images from mirrors are always inverted; an erect real image is not possible for a standard single mirror; Real, inverted, and diminished: real inverted images require the object to be beyond the focus; here the object is within the focal length.

Correct Answer: D. Reflectivity

• **Reflectivity** = Reflectivity (or reflectance) is the fraction of incident light energy reflected by a surface; a high reflectivity means the surface acts as a good mirror. • **0 to 1 scale** — polished silver has reflectivity near 0.95 in visible light; matte black paint has reflectivity near 0.03. • 💡 Wrong-option analysis: Viscosity: viscosity is a property of fluids describing resistance to flow and has nothing to do with light reflection; Refractive index: the refractive index describes how much light slows and bends when entering a transparent medium, not how much is reflected; Conductivity: conductivity describes the ability to conduct electricity or heat, not the ability to reflect light.

Correct Answer: A. Heavy curtains and acoustic panels

• **Heavy curtains and acoustic panels** = Soft porous materials absorb sound energy rather than reflecting it, reducing the number of reflections and therefore reverberation time. • **Absorption coefficient** — heavy curtains and foam panels have absorption coefficients of 0.4–0.9, far higher than hard surfaces like marble (0.01) or glass (0.03). • 💡 Wrong-option analysis: Metal sheets on walls: metal is a hard, non-porous material that reflects sound efficiently, increasing reverberation rather than reducing it; Polished marble walls: marble is smooth and hard, making it an excellent sound reflector and thus increasing reverberation; Large glass panels: glass is highly reflective to sound; glass panels would increase reverberation, not decrease it.

Correct Answer: D. 65°

• **65°** = The angle with the surface (grazing angle) and the angle of incidence (from normal) are complementary: i = 90° − 25° = 65°. • **Complementary angles** — the normal is perpendicular to the surface, so the angle of incidence = 90° − (angle with surface). • 💡 Wrong-option analysis: 25°: this is the glancing angle (from the surface), not the angle of incidence (from the normal); 45°: 45° would be correct only if the ray made 45° with the surface, not 25°; 75°: this is 90° − 15°, using the wrong complement.

Correct Answer: A. Multiple reflection between plane mirrors

• **Multiple reflection between plane mirrors** = In a kaleidoscope, two or three plane mirrors are placed at angles to each other; successive reflections produce a set of symmetric colourful images. • **60° arrangement** — mirrors at 60° produce (360/60 − 1) = 5 images symmetrically arranged, giving a hexagonal pattern; other angles give different numbers of images. • 💡 Wrong-option analysis: Total internal reflection only: total internal reflection occurs inside dense optical media like glass fibre, not between external plane mirrors in a kaleidoscope; Refraction through a lens only: a lens bends light by refraction; kaleidoscopes use reflection, not refraction; Diffraction through a slit: diffraction through a slit produces interference fringes and is used in spectroscopy, not in kaleidoscopes.

Correct Answer: C. Within the focal length

• **Within the focal length** = When the face is between the pole and the focus of a concave mirror, the reflected rays diverge and the image is virtual, erect, and magnified. • **u < f condition** — for an object closer than the focal length, the mirror formula gives a positive v (image behind mirror), confirming a virtual magnified image. • 💡 Wrong-option analysis: At infinity: an object at infinity gives a real image at the focus, which is tiny and inverted — useless for shaving; Beyond the center of curvature: beyond 2f the concave mirror gives a real, inverted, diminished image — also useless for shaving; Exactly at the focus: an object at the focus causes reflected rays to be parallel (image at infinity), not magnified.

Correct Answer: B. 50°

• **50°** = The reflected ray makes 40° with the normal; since the mirror surface is perpendicular to the normal, the angle between the reflected ray and the mirror surface = 90° − 40° = 50°. • **Complementary angle** — the angle from the normal and the angle from the surface are always complementary (sum = 90°); angle of incidence = angle with normal = 40°, so angle with surface = 50°. • 💡 Wrong-option analysis: 90°: 90° would mean the reflected ray is perpendicular to the surface, which only occurs at normal incidence (i = 0°); 40°: 40° is the angle the reflected ray makes with the normal, not with the mirror surface; 40° to the normal only: this is a true statement about the reflected ray and the normal, but the question asks for the angle with the mirror surface, which is 90° − 40° = 50°.

Correct Answer: D. Direction of propagation

• **Direction of propagation** = Reflection redirects the light ray; the component of velocity perpendicular to the mirror surface is reversed while the parallel component is unchanged. • **Angle change** — the direction change equals the angle between incident and reflected rays = 2i; the ray is re-directed but its frequency, speed, and wavelength are unaffected. • 💡 Wrong-option analysis: Frequency: frequency is a property of the photon and remains constant on reflection; changing frequency would change the colour; Speed in the same medium: speed of light in a given medium depends only on the medium, not on reflection direction; Wavelength in the same medium: since both frequency and speed are unchanged, wavelength = speed/frequency is also unchanged.

Correct Answer: D. +1

• **+1** = Magnification m = image height / object height = 3 / 3 = +1; the positive sign confirms the image is erect and the magnitude 1 confirms same size. • **Plane mirror property** = m = +1 always for a plane mirror regardless of object position, because the image is always virtual, erect, and the same size as the object. • 💡 Wrong-option analysis: −1: negative magnification means an inverted image; plane mirror images are always erect; 0: zero magnification means no image; +2: m = +2 would mean the image is twice the size of the object, which does not happen for a plane mirror.

Correct Answer: A. f = R/2

• **f = R/2** = For a spherical mirror of small aperture, rays parallel to the principal axis converge (or appear to diverge) at the midpoint between the pole and the centre of curvature, so f = R/2. • **Geometric derivation** — the reflected ray from any peripheral point passes through F midway between P and C because the reflected angle equals the incidence angle with respect to the radius at that point. • 💡 Wrong-option analysis: f = 2R: this inverts the relationship, making the focal length twice the radius, which is geometrically wrong for a spherical mirror; f = R: if f = R, the focus and centre of curvature would coincide, which contradicts the derivation; R = f/2: this rearranges to f = 2R, again the incorrect inverse of the correct relationship.