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Stand in front of a bathroom mirror and you can see your face but not your shoes. Step back and it feels as if you should see more of yourself. You do not. The rule that settles this, a mirror half your height, hung in the right place, is a favourite short question in ray optics and a good test of whether you can draw a ray diagram instead of guessing. This post derives the rule, shows where the mirror has to hang, and extends it to seeing something behind you.
Is this in the syllabus?
The JEE (Main) 2026 syllabus starts Unit 16, Optics, with "Reflection of light", and the NEET (UG) 2026 syllabus does the same. The JEE (Advanced) 2026 brochure lists "reflection and refraction at plane and spherical surfaces". The two facts you need are in NCERT. The Class 10 chapter Light – Reflection and Refraction says the image in a plane mirror is erect, the same size as the object, and "as far behind the mirror as the object is in front of it". The Class 12 chapter Ray Optics and Optical Instruments restates the laws of reflection. Both are 2026-27 reprints. The mirror-height problem itself is an application. Check your own year's syllabus.
Why is half your height enough?
Let your height be H, with your eyes a small distance below the top of your head. You stand at distance d from a vertical plane mirror, so your image stands at distance d behind it, 2d from your eyes.
To see your feet, a ray from your feet must reflect into your eye. Trace it backwards: the eye sees the image of your feet along a straight line from the eye to the image's feet. That line crosses the mirror at the midpoint, by similar triangles, because the mirror is exactly halfway between you and your image. So the lowest useful point of the mirror is at half your eye height.
The same argument for the top of your head puts the highest useful point halfway between your eye level and the top of your head. The distance between the two points is half of eye height plus half of the gap above the eyes, which is H/2.
Worked example 1: where to hang the mirror
These are sample numbers. You are 1.70 m tall and your eyes are 1.58 m above the floor.
Bottom edge: half of eye height, 1.58/2 = 0.79 m above the floor.
Top edge: eye height plus half the gap to the top of your head, 1.58 + 0.12/2 = 1.64 m.
Mirror length: 1.64 − 0.79 = 0.85 m, which is 1.70/2.
Now move. At 0.5 m, 1 m or 3 m from the mirror, the two crossing points stay at 0.79 m and 1.64 m, because every distance in the diagram scales together.
Why does it feel wrong?
You are not alone if your instinct said otherwise. Bertamini and Parks (2005) found that most people are unaware of the size of their own image on a mirror, and explored naive beliefs about how mirror images change with distance; their findings pointed to a difficulty in factoring in the observer's own viewpoint. In an earlier study, Bertamini, Spooner and Hecht (2003) asked undergraduates to predict when they would first see themselves while walking towards a mirror from the side; they expected to see their reflection earlier than they actually would. The cure for both is the same: draw the eye, the mirror and the image, and trust the straight lines.
Worked example 2: seeing a tree behind you
The same idea gives a general result. If your eye is at distance a from the mirror and an object of height h is at distance b from the mirror (on your side), its image is b behind the mirror, a + b from your eye. The strip of mirror you need is
length = h × a / (a + b)
For yourself, b = a and the length is h/2, the half-height rule.
Now, with sample numbers, a 6.0 m tree stands 8.0 m behind you and you stand 2.0 m from the mirror, so a = 2.0 m and b = 10.0 m. The strip needed is 6.0 × 2.0 / 12.0 = 1.0 m. With your eye at 1.6 m, the rays from the tree's base and top cross the mirror plane at about 1.33 m and 2.33 m, so a mirror that ends at head height will cut off the top of the tree.
What about curved mirrors?
The rule is for plane mirrors only. NCERT's Activity 9.6 in the Class 10 chapter asks you to look at a distant tree in plane, concave and convex mirrors, and notes that a full-length image of a tall building can be seen "in a small convex mirror", such as the one fitted in a wall of Agra Fort facing the Taj Mahal. A convex mirror makes a smaller, virtual image, so a smaller mirror can hold all of it.
Which mistakes cost marks?
Saying the mirror must be as tall as you. It needs half your height.
Saying the answer depends on distance. For yourself in a plane mirror, it does not.
Measuring the bottom edge from your height instead of your eye height. Use eye height / 2.
Drawing the reflected ray by eye. Use the image instead: a straight line from the eye to the image point crosses the mirror where the reflection happens.
Using the half rule for an object that is not at your own distance. Use h × a/(a + b).
A practice routine
Draw the full ray diagram for yourself at two distances, to scale on graph paper, and measure the strip.
Work out the minimum mirror width to see both shoulders, using the same argument sideways.
Redo example 2 with the tree 2.0 m behind you.
Try the related plane-mirror questions in our posts on image velocity in mirrors and images in two inclined mirrors.
To test the geometry rather than just read it, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read.
Tonight, stick two strips of tape on a mirror at home where the rule says your feet and head appear, and check it from two distances.
