Which one of the following statements is correct for a plane mirror?
- (a)Its focal length is zero.
- (b)The size of the image of an object placed in front of the mirror is slightly less than that of the object.
- (c)The image is virtual, erect and laterally inverted.
- (d)Its focal length is 200 cm.
Correct — C, The image is virtual, erect and laterally inverted. Those three words describe every plane-mirror image without exception. It is virtual because the reflected rays diverge and only appear to come from a point behind the mirror, so the image cannot be caught on a screen. It is erect because the top of the object stays the top of the image. And it is laterally inverted because the left of the object appears as the right of the image, which is why an ambulance carries its name reversed on the bonnet so that a driver ahead reads it correctly in a rear-view mirror. Two further properties complete the picture: the image is the same size as the object, and it lies as far behind the mirror as the object stands in front.
- (a)Its focal length is zero. — A plane mirror can be thought of as a spherical mirror of infinite radius of curvature, and since f = R/2, its focal length is infinite, not zero. A focal length of zero would mean the mirror converged parallel light to a point on its own surface.
- (b)The size of the image of an object placed in front of the mirror is slightly less than that of the object. — The magnification of a plane mirror is exactly one, so the image is precisely the same size as the object however near or far the object is placed. Nothing about a plane mirror shrinks the image.
- (d)Its focal length is 200 cm. — This assigns a finite, arbitrary number to a mirror that has no curvature at all. A specific focal length belongs to a curved mirror; for a flat one it is infinite.
Reflection at a plane surface obeys the same two laws as reflection anywhere else — the angle of incidence equals the angle of reflection, and the incident ray, the reflected ray and the normal lie in one plane. Because the surface is flat, parallel rays stay parallel after reflection, so no real focus is formed. Tracing the reflected rays backwards shows that they appear to diverge from a point exactly as far behind the mirror as the object is in front, and that construction is what produces every property of the image.
Three of the four options here are about numbers and only one is about the nature of the image, which is a hint in itself. Two options offer competing focal lengths, and they cannot both be right; noticing that a flat surface has no centre of curvature settles both at once, because R is infinite and therefore so is f. Lateral inversion is worth understanding rather than memorising: the mirror does not swap left and right so much as reverse the direction perpendicular to its surface, and our habit of describing a person as turning to face us converts that front-back reversal into an apparent left-right one. The everyday tests are the ambulance lettering and the way a clock read in a mirror shows the time as 12 minus the true reading.
- A plane-mirror image is virtual, erect, laterally inverted, of the same size as the object, and as far behind the mirror as the object is in front.
- The magnification of a plane mirror is exactly +1.
- For a spherical mirror f = R/2; a plane mirror has infinite radius of curvature and therefore infinite focal length.
- To see his full height, a person needs a plane mirror only half as tall as himself, whatever his distance from it.
Only the statement about the nature of the image survives; the two focal-length options contradict each other and both fail.
- Treating a plane mirror's focal length as zero because the mirror is flat; flatness means infinite radius, hence infinite focal length.
- Thinking the image shrinks as the object moves away, as it appears to do with distance in everyday sight; the image size is fixed and equal to the object.
- Calling a plane-mirror image inverted; it is laterally inverted, which is not the same as being upside down.
Asked as a single-correct-statement item where two of the distractors offer rival numerical values for the same quantity.
When a mirror is rotated by an angle of θ, the reflected ray will rotate by
- (a) 0°
- (b) θ / 2
- (c) θ
- (d) 2θ
Answer(d) 2θ
Works the same plane surface from the ray-geometry side. Both the angle of incidence and the angle of reflection change by θ when the mirror turns, which is the same law of reflection that fixes the image's position here.
The correct relation between the radius of curvature R and focal length f of a spherical mirror is
- (a) R = f
- (b) R = 2f
- (c) R = 3f
- (d) R = 4f
Answer(b) R = 2f
Supplies the relation that disposes of both focal-length distractors here. A flat mirror has infinite R, so f = R/2 is infinite rather than zero or any stated number.
If the image of an object, formed by a concave mirror is virtual, erect and magnified, then the object is placed
- (a) at the principal focus
- (b) at the centre of curvature
- (c) beyond the centre of curvature
- (d) between the pole of the mirror and the principal focus
Answer(d) between the pole of the mirror and the principal focus
Uses the same vocabulary of virtual and erect but for a curved mirror, where the position of the object decides everything. The contrast shows why the plane mirror's answer needs no condition attached.
- practice — not a real PYQ
A person stands 2 m in front of a plane mirror. The distance between the person and his image is
- (a)1 m
- (b)2 m
- (c)4 m
- (d)It depends on the size of the mirror
Answer(c) 4 m — the image lies 2 m behind the mirror, as far behind as the object is in front, so the two are 4 m apart.
- practice — not a real PYQ
The minimum height of a plane mirror needed for a person to see his full image is
- (a)equal to his height
- (b)half his height
- (c)one-third of his height
- (d)twice his height
Answer(b) half his height — and the result does not change with how far he stands from the mirror.