Move the candle and see how a mirror bounces light and where the image forms. Then turn and slide mirrors to steer lasers, sunlight and starlight in a 12-level puzzle game.
Drag the candle (or use the slider) and watch the special rays bounce off the mirror and find the image. Switch between a concave, a convex and a plane mirror and change the focal length to see the image move, flip and change size.
Parallel to the axis → through FThrough F → parallelThrough C → straight backTo the vertex → same angle outRays from the candle tipNormal (angles are measured from it)Traced back behind the mirror (virtual image)
Object distance a
Image distance b
Magnification
Image height (object 4 cm)
Pick a mirror from the tray and it goes onto a free stand (tap an empty stand first to choose it). Drag a mirror on a stand to turn it, or along a dashed rail to slide it. Keyboard: Enter selects, ←/→ slide or turn, Q/E turn, Delete removes. Three stars for using the fewest mirrors without a hint.
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The law of reflection
When light hits a smooth, shiny surface it bounces off in a completely predictable way. Draw a line at right angles to the surface where the light lands — the normal. The angle between the incoming ray and the normal is the angle of incidence, the angle between the outgoing ray and the normal is the angle of reflection, and the two are always equal. The incoming ray, the outgoing ray and the normal also lie in one flat plane.
Because the angles are measured from the normal, turning a mirror changes both of them at once. Tilt a mirror by 10° and the reflected beam swings by 20°, which is why a small wobble of a mirror sends a spot of light racing across a wall. Level 1 of the puzzle is built on this: the mirror's normal has to sit exactly halfway between where the light comes from and where it has to go.
Plane mirrors: the room behind the glass
Light from the tip of the candle spreads out, hits a flat mirror and bounces back still spreading. Your eye cannot tell that the light has turned a corner, so it traces the rays straight back and sees them coming from a point behind the glass. Following those dashed lines in the lab always leads to the same place: an upright image of the same size, exactly as far behind the mirror as the candle is in front of it.
No light actually travels behind the mirror, so this is a virtual image — you can see it, but a sheet of paper held there stays dark. A plane mirror does not really swap left and right; it swaps front and back, which is why mirror writing looks reversed. Two plane mirrors at 45° make a periscope, and two at a right angle send any beam straight back, the idea behind bike reflectors.
Concave mirrors gather light
A concave mirror curves inward, like the inside of a spoon. Light arriving parallel to its axis bounces toward the axis and meets at the focal point F in front of the mirror. The mirror is a slice of a sphere, and the center of that sphere is the center of curvature C. For a gently curved mirror the focal point lies halfway to C, so the focal length is half the radius: f = R/2.
Depending on where the object stands, a concave mirror does very different jobs. Far beyond C it makes a small, upside-down real image near F — the principle of the reflecting telescope and the solar cooker. At C the image is the same size and upside down, right on top of the object. Between F and C it is enlarged and upside down, out beyond C. At F the light leaves as a parallel beam, which is how a flashlight works. Inside F you see an upright, enlarged virtual image behind the mirror: a makeup or shaving mirror.
Convex mirrors spread light
A convex mirror bulges outward, like the back of a spoon. Parallel light bounces off it spreading apart, as if it came from a focal point behind the mirror, so its focal length is written as a negative number. The reflected rays never meet in front of the mirror, so wherever the object is, the image is virtual, upright and smaller, and it sits between the mirror and its focal point.
Shrinking the image is exactly what makes a convex mirror useful: a small mirror can show a very wide area. Car side mirrors, the round mirrors at blind corners and shop security mirrors are all convex. The catch is that everything looks smaller, and therefore farther away, than it really is — the reason many passenger-side mirrors carry the warning that objects are closer than they appear.
Finding the image with special rays
Every point of the candle sends light everywhere, but four rays off a curved mirror are easy to predict, and any two of them find the image of the tip. In the lab they are drawn in four colors. A ray parallel to the axis reflects through F (red). A ray through F reflects parallel to the axis (blue). A ray through C hits the mirror head-on and comes straight back (purple). A ray to the vertex, the center of the mirror, leaves at the same angle on the other side of the axis (yellow).
Where the reflected rays really cross, in front of the mirror, a real image forms. When they spread apart, trace them backwards as dashed lines behind the mirror; the point where the dashed lines meet is a virtual image. For a convex mirror F and C lie behind the glass, so the parallel ray leaves as if it came from F, and the ray aimed at C behind the mirror bounces straight back.
The mirror equation
The ray diagram turns into the same short equation used for lenses. With a the distance from the object to the mirror, b the distance from the mirror to the image and f the focal length, 1/f = 1/a + 1/b, and the magnification is m = −b/a. For mirrors the signs work like this: b is positive when the image is in front of the mirror (real) and negative when it is behind (virtual); f is positive for a concave mirror and negative for a convex one.
Take a concave mirror with f = 10 cm and a candle 15 cm away: 1/b = 1/10 − 1/15 = 1/30, so the image is 30 cm in front of the mirror, and m = −2 — twice as tall and upside down. Move the candle to 5 cm: 1/b = 1/10 − 1/5 = −1/10, so b = −10 cm, a virtual image 10 cm behind the glass, upright and twice as tall. A plane mirror is the limit of a very flat curve, with 1/f = 0, which gives b = −a and m = 1. Every number in the lab and the quiz comes straight out of these two formulas.
Mirrors and lenses: same equation, opposite sides
A lens bends light as it passes through, so real images form on the far side of the lens; a mirror sends light back, so real images form on the same side as the object. Apart from that the two families mirror each other: a concave mirror gathers light like a convex lens, and a convex mirror spreads it like a concave lens. The names flip because a lens is named by its shape as a solid piece of glass, a mirror by the shape of its reflecting surface.
Mirrors have one big advantage: every color reflects at exactly the same angle, while glass bends blue light a little more than red. That is why the largest telescopes use mirrors. Newton built his reflecting telescope in 1668 partly to escape the colored fringes of lens telescopes, and level 11 of the puzzle rebuilds it. If you want the lens side of the story, try the Convex and Concave Lens Lab.
About this simulator
The lab and the quiz use the textbook model of a thin spherical mirror. Rays are treated as paraxial — close to the axis — so every number follows exactly from 1/f = 1/a + 1/b and m = −b/a, and the mirror is drawn only slightly curved. Real spherical mirrors blur a little at the edges (spherical aberration), which is why big telescopes use parabolic mirrors.
In the puzzle, plane mirrors reflect exactly by the law of reflection and work on both sides.
Curved mirrors in the puzzle are ideal mirrors that focus perfectly; only their front face reflects, and the back blocks light.
Your stars and your quiz difficulty are saved only in this browser.
Why does a mirror flip left and right but not up and down?
It actually flips neither. A plane mirror reverses front and back: your nose points toward the mirror while your image's nose points back at you. We describe it as a left–right swap because we imagine turning around to stand where the image is, and people turn around a vertical axis. Lie on your side in front of a mirror and the 'flip' seems to be up and down instead.
What is the difference between a real image and a virtual image?
A real image forms where reflected light actually meets, so you can catch it on a sheet of paper; with a mirror it always lies in front of the glass and is upside down. A virtual image is where light only seems to come from when you trace it backwards. You can see it by looking into the mirror, but a sheet of paper behind the mirror stays dark. In the lab, real images are drawn solid and virtual ones dashed.
Why are objects in a car's side mirror closer than they appear?
Many passenger-side mirrors are convex so they can show a wider stretch of road. A convex mirror always makes a smaller virtual image, and your brain reads a small car as a distant car. Set the lab to a convex mirror and drag the candle: the image always stays upright and shrunken, sitting close behind the glass.
How is a concave mirror different from a convex lens?
Both gather light and follow the same equation, 1/f = 1/a + 1/b, and both give the same sequence of images as the object moves closer. The difference is the side: a lens forms real images behind it, a mirror forms them in front of it, on the object's side. A mirror also reflects every color at the same angle, so it does not make the colored fringes that a simple lens does.
How do I solve the mirror puzzle levels?
Pick a mirror from the tray and it lands on a free stand or rail. Drag a mirror on a round stand to turn it, or along a dashed rail to slide it; on a keyboard, use Enter to select, the arrow keys to slide or turn, and Q and E to turn. The meter under the board shows how close you are. The hint button marks each mirror's normal and focal point and gives a clue, at the cost of one star.
What level of science is this for?
The law of reflection and plane mirrors come up in middle-school science, and the mirror equation with ray diagrams belongs to the optics unit of high-school physics. The puzzle needs no formulas at all, so anyone can play it, while the hard quiz level practices the mirror equation with real numbers.