Reflection — Set 6

Correct Answer: A. Virtual, erect, and same size

• **Virtual, erect, and same size** = A plane mirror forms a virtual image (reflected rays only appear to meet behind the mirror), erect (same orientation as object), and the same size (m = +1). • **m = +1 always** — the magnification for a plane mirror is always +1 regardless of object position, distance, or size. • 💡 Wrong-option analysis: Virtual, inverted, and same size: plane mirror images are always erect, not inverted; inversion requires a converging mirror with the object beyond the focus; Real, erect, and magnified: real images from mirrors are always inverted; an erect real image is not possible from a plane mirror; Real, inverted, and diminished: plane mirrors never form real images; the rays only appear to meet behind the mirror.

Correct Answer: D. Angle of incidence equals angle of reflection

• **Angle of incidence equals angle of reflection** = The first law of reflection states that the angle of incidence (i) equals the angle of reflection (r), both measured from the normal at the point of incidence. • **i = r** — this equality holds for all smooth reflecting surfaces regardless of the material, wavelength, or angle of incidence. • 💡 Wrong-option analysis: Incident ray, reflected ray, and normal lie in the same plane: this is the second law of reflection, not the first; Angle of reflection is always 90°: if r were always 90°, the reflected ray would lie along the surface, which only happens at grazing incidence (i ≈ 90°); Reflection happens only from mirrors: reflection occurs from any surface including water, glass, and rough walls; mirrors are polished surfaces that give specular reflection.

Correct Answer: A. Virtual and diminished

• **Virtual and diminished** = A convex mirror diverges reflected rays, producing a smaller virtual image; the diminished image allows a wider scene to fit within the mirror's field of view. • **Used as a rear-view mirror** — the diminished virtual image of a wide area behind allows a driver to see a large region in a small mirror, though objects appear farther than they are. • 💡 Wrong-option analysis: Virtual and magnified: convex mirrors always produce diminished images, never magnified ones; a magnified virtual image would require a concave mirror; Real and enlarged: convex mirrors cannot form real images since diverging reflected rays never actually meet; Real and same size: convex mirrors form only virtual images; real images require converging reflected rays.

Correct Answer: D. Principal focus

• **Principal focus** = Rays from a very distant object are parallel to the principal axis; a concave mirror converges them at the principal focus F. • **Telescope mirror principle** — this is how a large concave mirror in a reflecting telescope focuses starlight; the image at F is real, inverted, and highly diminished. • 💡 Wrong-option analysis: Pole: the pole is the geometric centre of the mirror surface, not a convergence point for parallel rays; Center of curvature: parallel rays converge at the focus (R/2 from pole), not at the centre of curvature (R from pole); Behind the mirror: images behind the mirror are virtual; real convergence of parallel rays occurs in front at the focus.

Correct Answer: C. Principal axis

• **Principal axis** = The principal axis is the straight line passing through the pole P and the centre of curvature C of a spherical mirror; it is the axis of symmetry of the mirror. • **Reference line** — all standard ray diagrams and mirror calculations use the principal axis as the horizontal reference; object and image distances are measured along it. • 💡 Wrong-option analysis: Aperture: the aperture is the diameter of the usable mirror surface, not a line; Normal: the normal at any point on the mirror is perpendicular to the surface there; only at the pole does the normal coincide with the principal axis; Focal plane: the focal plane is a plane perpendicular to the principal axis passing through the focus, not the axis itself.

Correct Answer: B. Focal length

• **Focal length** = The focal length f is defined as the distance from the pole P to the principal focus F measured along the principal axis; f = R/2 for a spherical mirror. • **Convergence power** — a shorter focal length means the mirror bends rays more steeply; f determines whether the mirror is strongly or weakly converging. • 💡 Wrong-option analysis: Aperture: aperture is the width (diameter) of the mirror opening, unrelated to the focal distance; Radius of curvature: the radius of curvature R is the distance from the pole to the centre of curvature C, which equals 2f; Optical path length: optical path length is the product of geometric distance and refractive index, a concept in interference, not a mirror dimension.

Correct Answer: C. Reflected rays actually meet at a point

• **Reflected rays actually meet at a point** = A real image forms where reflected rays physically converge; placing a screen at that point captures the light energy and makes the image visible. • **Real vs virtual** — virtual images (formed by plane mirrors or a concave mirror when object is within f) cannot be captured on a screen because rays only appear to meet when extended backward. • 💡 Wrong-option analysis: The mirror absorbs light: mirrors are designed to reflect, not absorb; absorption would reduce brightness, not create a screened image; It is laterally inverted: lateral inversion is a property of plane mirror virtual images; it does not explain why real images can be caught on a screen; The image is always behind the mirror: virtual images form behind the mirror; real images form in front and can be projected onto a screen.

Correct Answer: D. Apparent intersection of reflected rays when extended backward

• **Apparent intersection of reflected rays when extended backward** = Reflected rays from a plane mirror diverge in front; an observer's brain traces them back in straight lines until they intersect behind the mirror, locating the virtual image. • **Virtual image definition** = An image is virtual when it is formed by backward extensions of rays, not by actual convergence; the plane mirror image cannot be captured on a screen. • 💡 Wrong-option analysis: Actual convergence of reflected rays behind the mirror: actual convergence behind the mirror would produce a real image there, but plane mirror images are virtual; Absorption of light by the mirror: mirrors reflect light; absorption would reduce intensity but does not create any image; Refraction of light inside the mirror: refraction occurs when light crosses from one transparent medium to another; reflection from a mirror surface does not involve refraction.

Correct Answer: B. 20 cm

• **20 cm** = f = R/2 = 40/2 = 20 cm; the focal length is always half the radius of curvature for a spherical mirror. • **R = 40 cm → f = 20 cm** — the principal focus is midway between the pole and the centre of curvature, so the distance from pole to focus is exactly half of R. • 💡 Wrong-option analysis: 10 cm: this is R/4, obtained by dividing by 4 instead of 2; 40 cm: this equals R itself, confusing the radius of curvature with the focal length; 15 cm: this has no mathematical relationship to R = 40 cm.

Correct Answer: D. Negative

• **Negative** = In the new Cartesian sign convention, all distances are measured from the pole; incident light travels in the negative x-direction toward the mirror, so object distance u is negative for a real object in front. • **Sign convention rule** — distances measured in the direction of incident light are positive; a real object is placed on the same side as the incident light, which is the negative direction from the pole. • 💡 Wrong-option analysis: Positive: positive u would place the object behind the mirror, implying a virtual object (not the standard case); Zero: zero u means the object is at the pole itself, which is a degenerate case; Always infinite: infinite u means the object is at infinity, which is only one specific scenario, not the general case.