Consider the following figure : [FIGURE: a step-shaped arrow labelled Object on the left, and a vertical hatched line labelled Mirror (Plane) on the right — see figure_note] Which one of the following is the image of the object in the mirror?
- (a)[FIGURE] The same step shape MIRRORED LEFT-TO-RIGHT: the upper horizontal segment is on the RIGHT and its right-hand free end carries the open chevron barb (opening rightwards); the line drops vertically at the left end of that upper segment, then runs LEFT along the lower level and ends in a solid arrowhead pointing LEFT.
- (b)[FIGURE] Exactly the same shape and orientation as the object drawn in the stem: upper horizontal segment on the LEFT with the open chevron barb at its left-hand free end, a vertical drop at its right end, then a lower horizontal running RIGHT and ending in a solid arrowhead pointing RIGHT.
- (c)[FIGURE] The same step shape FLIPPED TOP-TO-BOTTOM, so that it steps UP instead of down: the horizontal segment carrying the open chevron barb at its left-hand free end is now the LOWER one; the line rises vertically at its right end, then runs RIGHT along the upper level and ends in a solid arrowhead pointing RIGHT.
- (d)[FIGURE] The same step shape and the same downward step as the object, but with the two end marks EXCHANGED: the upper horizontal on the LEFT ends in a SOLID ARROWHEAD pointing LEFT, and the lower horizontal on the RIGHT ends in the OPEN CHEVRON barb (opening rightwards).
Answer
Why
Correct — A, (a) the drawing in which the whole step shape is reversed left to right — the barbed end now at the far side and the solid arrowhead at the near side, pointing back towards the mirror. A word first about what is printed. This question carries a figure in the stem and four more figures as its options, and the options have no text on them at all: the booklet prints the letters (a) to (d) down the column with a line drawing beside each. The words in the option list here are a transcription written so that the four drawings can be told apart in print; they are not wording the Commission printed. In the stem the object is a step-shaped line — an upper horizontal segment on the left whose free end carries a small open chevron barb, a vertical drop at the right-hand end of that segment, and a lower horizontal running further right and finishing in a solid arrowhead. To the right of it stands the mirror, drawn as a vertical line hatched along its far side, so its reflecting face looks left towards the object. The two italic labels, Object and Mirror (Plane), are the only words inside the figure.
A plane mirror reverses one direction only: the one at right angles to its surface. This mirror is vertical and faces sideways, so left and right are exchanged in the image while up and down are untouched. Everything else is preserved — the image is the same size as the object, it is the same way up, and every point of it lies as far behind the mirror as the corresponding point of the object lies in front.
Apply that to the step. The upper segment, which lies on the left in the object, must lie on the right in the image, and the barbed free end goes with it to the far side. The lower segment must run leftwards, and the solid arrowhead at its end must point left — that is, back towards the mirror, exactly as the arrowhead in the object points right towards it. The step still goes downwards, because up and down do not change. Only the first drawing has all three of these features, so the answer is option (a).
The quickest discriminator, and the one to use under time pressure, is the near end. In the object the solid arrowhead is the part closest to the mirror; distances from the mirror are preserved by reflection, so the solid arrowhead must still be the part closest to the mirror in the image, while the barb stays farthest from it.
Why the others are wrong
- (b)[FIGURE] Exactly the same shape and orientation as the object drawn in the stem: upper horizontal segment on the LEFT with the open chevron barb at its left-hand free end, a vertical drop at its right end, then a lower horizontal running RIGHT and ending in a solid arrowhead pointing RIGHT. — This drawing is the object copied rather than reflected: the upper segment is still on the left with the barb at its left-hand end, and the lower segment still runs right to a solid arrowhead pointing right. A plane mirror never produces such an image from an object like this one. Lateral inversion is not optional and does not depend on how the object is held; it follows from the geometry of reflection, in which every point is carried straight across the mirror plane to a point the same distance behind. The only objects whose reflections look unchanged are those already symmetrical about a line parallel to the mirror — the letters A, H, I, M, O, T, U, V, W, X and Y in a vertical mirror, for instance. This step shape is not symmetrical in that way, since one end carries a barb and the other an arrowhead, so its image must differ visibly from it.
- (c)[FIGURE] The same step shape FLIPPED TOP-TO-BOTTOM, so that it steps UP instead of down: the horizontal segment carrying the open chevron barb at its left-hand free end is now the LOWER one; the line rises vertically at its right end, then runs RIGHT along the upper level and ends in a solid arrowhead pointing RIGHT. — Here the shape has been turned upside down: the barbed segment has become the lower one and the figure steps upwards instead of downwards, while left and right are unchanged. That is the image a horizontal mirror would give — a mirror lying flat below or above the object, like the surface of still water, whose perpendicular direction is the vertical one. The mirror in this question is vertical, so the direction it reverses is the horizontal one, and the up-down arrangement of the figure survives untouched. Choosing this drawing means applying the right principle about the wrong axis. The safeguard is to look at the mirror before looking at the object and to say which way it faces: the axis a plane mirror reverses is always the one at right angles to its own surface, and nothing else.
- (d)[FIGURE] The same step shape and the same downward step as the object, but with the two end marks EXCHANGED: the upper horizontal on the LEFT ends in a SOLID ARROWHEAD pointing LEFT, and the lower horizontal on the RIGHT ends in the OPEN CHEVRON barb (opening rightwards). — This drawing keeps the outline of the object exactly as it was — upper segment on the left, step downwards, lower segment on the right — and merely exchanges the two end symbols, putting the solid arrowhead at the far left and the barb at the near right. It is not a reflection of anything. Reflection moves every point of the figure across the mirror plane, so the outline itself has to reverse; an image cannot keep the object's arrangement and swap only its details. The exchange it does make is also the wrong way round on the test that matters most. In the object the solid arrowhead is the feature nearest the mirror, and reflection preserves distance from the mirror, so the arrowhead must remain the nearest feature in the image. This drawing sends it to the far end and brings the barb close, which is the opposite of what reflection does.
Concept
The image formed by a plane mirror has four properties, and school physics states them together: it is virtual and erect, it is the same size as the object, it lies as far behind the mirror as the object lies in front of it, and it is laterally inverted. Lateral inversion is the one that decides picture questions, and it is best understood not as 'left and right are swapped' but as 'the direction perpendicular to the mirror is reversed, and no other'. For an ordinary wall mirror that perpendicular direction is the horizontal one running towards the glass, which is why writing appears backwards while the ceiling stays overhead. For a mirror lying flat, as a still pool does, the reversed direction is the vertical one, which is why a reflected building appears upside down but not left-right swapped. The consequences for a drawn figure are exact and easy to apply: measure each feature's distance from the mirror and keep it, then reverse the order of features along the perpendicular direction while leaving their positions along the mirror unchanged. A figure that is symmetrical about a line parallel to the mirror looks unaltered in the image, which is why some capital letters survive reflection and others do not.
The Commission puts only two figure-based items in this paper, at questions 109 and 118, and they test complementary skills — the first, whether a candidate can read a logical relationship out of a picture, and this one, whether a candidate can apply a physical rule to a picture. Mirror-image items are a standing feature of reasoning sections in recruitment papers generally, and they are set because they cannot be answered by recall: the rule is one sentence long and everything depends on applying it accurately to a particular asymmetric shape. Two habits make them quick. The first is to identify the mirror's orientation and state, in words, which direction it reverses. The second is to choose a single distinguishing feature of the object — here the solid arrowhead, which is the part nearest the mirror — and to track where that one feature must end up, rather than trying to reconstruct the whole image in the head. A single well-chosen feature usually eliminates three of the four drawings at once.
Key facts
- The image in a plane mirror is virtual and erect, the same size as the object, and as far behind the mirror as the object is in front of it.
- The image is laterally inverted: a plane mirror reverses the direction perpendicular to its own surface and no other direction.
- The mirror in this figure is vertical, so left and right are exchanged while the up-down arrangement is unchanged.
- The step therefore still steps downwards in the image, but the segment that was on the left appears on the right.
- Distance from the mirror is preserved, so the feature nearest the mirror in the object is nearest to it in the image.
- In the object the solid arrowhead is the nearest feature and the open chevron barb the farthest; the image keeps that order.
- A figure symmetrical about a line parallel to the mirror looks unchanged in the image, which is why letters such as A, H and O survive reflection.
- The standard drawing convention for a plane mirror is a line hatched on its back side, so the unhatched face is the reflecting one.
Study next
Common traps
- Turning the figure upside down when the mirror is vertical; a vertical mirror never changes up and down.
- Copying the object unchanged, which would be the image only of a figure already symmetrical about a line parallel to the mirror.
- Swapping the details of a figure while leaving its outline as it was, which no reflection can produce.
- Ignoring distance from the mirror, when the nearest feature of the object must remain the nearest feature of the image.
- Reading the hatching on the mirror symbol as the reflecting side, when it is drawn on the back.
Mirror-image questions come in three regular forms. The first, as here, gives a drawn figure and a mirror and asks which of four drawings is the image. The second gives a word, a number or a clock face and asks how it appears in a mirror, which is answered by reversing the order of the characters and then each character in turn. The third gives a mirror in an unusual position — below the object, or at the top of the page — and rewards the candidate who has understood that the reversed direction is always the one at right angles to the mirror rather than the horizontal one by default. Since the options in this family are pictures, the discipline that saves time is to fix one asymmetric feature of the object, decide where reflection must send it, and discard every drawing that puts it somewhere else.
Related PYQs
EPFO_EOAO_2017_Q109Open & attempt →Which one of the following diagrams is most appropriate to the statement, “Tea-producing places are either in Assam or in Bengal”?
- (a) [FIGURE] One large ellipse with two separate rectangles drawn inside it, side by side; the two rectangles do not touch each other or the ellipse.
- (b) [FIGURE] Two rectangles side by side with a clear gap between them, plus an ellipse straddling the RIGHT-HAND EDGE of the left rectangle — roughly half the ellipse lies inside that left rectangle and the other half projects into the gap. The ellipse does not reach the right-hand rectangle, and the two rectangles do not touch.
- (c) [FIGURE] Two rectangles side by side with a gap between them, plus an ellipse centred ON THE GAP so that it overlaps BOTH rectangles — its left part crosses into the right end of the left rectangle and its right part crosses into the left end of the right rectangle. The two rectangles themselves do not touch.
- (d) [FIGURE] ONE rectangle divided into two halves by a vertical line down its middle, with an ellipse centred on that dividing line and lying wholly inside the rectangle, so that half the ellipse falls in each half of the rectangle.
Answer(d) [FIGURE] ONE rectangle divided into two halves by a vertical line down its middle, with an ellipse centred on that dividing line and lying wholly inside the rectangle, so that half the ellipse falls in each half of the rectangle.
The only other question in this paper whose options are drawings, nine items earlier — which arrangement of regions represents a statement about tea-producing places.
EPFO_APFC_2023_Q54An object is placed in front of a concave mirror at infinity. Which one of the following is correct for its image?
- (a) A real and inverted image would be formed at the focal point.
- (b) A virtual and inverted image would be formed at the focal point.
- (c) A real and erect image would be formed at infinity.
- (d) A virtual and erect image would be formed at the focal point.
Answer(a) A real and inverted image would be formed at the focal point.
Reflection at a curved surface instead of a flat one: the image formed by a concave mirror when the object is at infinity.
Practice
- practice — not a real PYQ
A capital letter is held before a vertical plane mirror. Which one of the following letters appears unchanged in the image?
- (a)B
- (b)A
- (c)F
- (d)P
Answer(b) A
- practice — not a real PYQ
The image of an object formed by a plane mirror is
- (a)real, inverted and of the same size as the object
- (b)virtual, erect and of the same size as the object
- (c)real, erect and larger than the object
- (d)virtual, inverted and smaller than the object
Answer(b) virtual, erect and of the same size as the object