Sita, 1·5 m high, stands before a plane mirror fixed on a wall to view her full image. What should be the minimum height of the plane mirror so that Sita can view her image fully ?
- (a)0·50 m
- (b)0·35 m
- (c)0·75 m
- (d)0·25 m
Correct — C, 0.75 m. A plane mirror needs to be only half as tall as the person standing in front of it. Trace two rays. Light from the top of her head must reach her eyes after one reflection, and because the angle of incidence equals the angle of reflection, the point where it strikes the mirror lies exactly halfway in height between her eyes and the top of her head. Light from her feet reaches her eyes off a point exactly halfway in height between her eyes and the floor. Every other part of her body sends light to the mirror between those two points, so the strip of mirror that is actually doing any work runs from the lower midpoint to the upper midpoint. That strip spans half the head-to-foot distance — half of 1.5 m, which is 0.75 m.
- (a)0·50 m — This is one-third of her height. No ray construction gives a third; the two midpoints fixed by the equal-angle rule always mark off exactly one half of the object's height, so 0.50 m would leave part of her image outside the mirror.
- (b)0·35 m — This is not a simple fraction of 1.5 m at all and corresponds to no step in the geometry. It appears to be a plausible-looking small number, and a mirror this short would cut off both her head and her feet.
- (d)0·25 m — This is one-sixth of her height, far too small. The mirror strip between the two reflection points is fixed at half the height regardless of how the person is proportioned, so a quarter-metre mirror shows only a small band of her body.
A plane mirror forms a virtual, erect image of exactly the same size as the object, standing as far behind the mirror as the object is in front of it. To see any part of yourself you need mirror at the point where the ray from that part reflects towards your eye, and the equal-angle law of reflection puts that point midway in height between the part and your eye. Collecting all such points gives a working strip exactly half the person's height.
The result surprises students twice over. First, most people expect a full-length mirror to be full length. Second, the answer does not depend on how far away she stands — walking closer or further changes where the reflection points sit horizontally but not the vertical span between them, so the minimum height stays at half. What does matter is placement — the useful strip has to be hung so that its top edge is at the mid-height between her eyes and the top of her head.
- A plane mirror gives a virtual, erect image of the same size as the object, formed as far behind the mirror as the object is in front.
- The minimum height of a plane mirror needed to see one's full image is half the person's height.
- For a person 1.5 m tall the minimum mirror height is 0.75 m.
- This minimum is independent of the distance between the person and the mirror.
- Assuming the mirror must be as tall as the person.
- Assuming the answer changes with the distance from the mirror — it does not.
- Forgetting that the half-height strip still has to be hung at the right level on the wall.
NDA asks either for the minimum mirror size for a full-length view, or for the nature of the image in a plane mirror — half the height, and virtual, erect, same size and laterally inverted.
The image of an object formed by a plane mirror is
- (a) erect, real and larger.
- (b) erect, virtual and same size.
- (c) inverted, virtual and same size.
- (d) inverted, real and smaller.
Answer(b) erect, virtual and same size.
States the property this question is built on — because the image is the same size as the object, the mirror still only needs to be half as tall, which is what makes the result counter-intuitive.
The image we see in a plane mirror is
- (a) real and thus can be photographed.
- (b) virtual and nearer than the object.
- (c) virtual and is laterally inverted.
- (d) real but cannot be photographed.
Answer(c) virtual and is laterally inverted.
Same plane-mirror image properties from another angle, covering the virtual nature and lateral inversion that accompany the same-size result used here.
- practice — not a real PYQ
A man 1.8 m tall wants to see his complete image in a plane mirror fixed on a wall. The minimum height of the mirror required is
- (a)1.8 m
- (b)1.2 m
- (c)0.9 m
- (d)0.6 m
Answer(c) 0.9 m — the minimum height of a plane mirror needed for a full-length view is half the person's height.
- practice — not a real PYQ
As a person walks towards a plane mirror on a wall, the minimum height of mirror needed to see her full image
- (a)increases
- (b)decreases
- (c)remains the same
- (d)first increases and then decreases
Answer(c) remains the same — the half-height result comes from the equal-angle rule and is independent of the distance from the mirror.