TwiddleLab / Physics / Light and Sight
Mirrors: Angle In, Angle Out
What you will learn
- Law of reflection: the angle in equals the angle out, both measured from the normal (the line at 90° to the mirror).
- Turn a mirror by some angle and the reflected beam turns by twice that angle.
- The image in a flat mirror is a virtual image: as far behind the glass as the object is in front. A full-length mirror only needs to be half your height, at any distance.
How the lesson goes
How tall must a mirror be to see your whole body?
You are 170 cm tall. Does stepping back help?
Turn the mirror to send the laser to the target.
The dashed line is the normal, at 90° to the mirror. Watch the two angles as you turn.
Where is the image in a mirror? Put it on the circles.
Drag the toy. The red ray bounces into the eye; the dashed line shows where it seems to come from.
The law of reflection.
The normal is the line at 90° to the mirror where the ray hits.
Law of reflection: angle of incidence = angle of reflection, both measured from the normal.
A flat mirror makes a virtual image: the reflected rays only seem to come from a point behind the glass, as far behind as the object is in front.
Simplified: we treat the mirror as perfect. Real mirrors absorb a few percent of the light.
Game: Laser maze. Turn the mirrors to light every target.
Three rooms. Drag the white knob on each mirror to turn it. Fewer moves, more stars.
Which things can you see in the mirror from where you stand?
Picture each thing's image straight across the mirror wall. Draw a line from your eye to that image. If the line passes through the mirror, a real ray from the thing bounces there into your eye.
Math: a mirror image is a reflection in a line.
Which copy is the blue shape's mirror image? Fold it to compare, then tap that copy.
A reflection keeps each point's distance to the line but puts it on the other side. With the line as the y-axis, x changes sign and y stays: (x, y) to (-x, y). A slide (translation) keeps the shape facing the same way, which a mirror never does.
Back to the start: size the mirror so you see all of yourself.
Use as little mirror as you can. Then step back and forth.
Light from your feet hits the mirror halfway between your eyes and your feet, then bounces up into your eyes (angle in = angle out). Light from the top of your head hits halfway between your eyes and the top of your head. The mirror only needs to span those two halfway points: half your height. Stepping back changes both triangles in the same ratio, so the halfway points stay put.
Speed round: where will the beam hit?
Four shots. Tap fast.
Previous lesson: Light Travels in Straight Lines · Next lesson: Refraction: Light Bends · Part of the course: Light and Sight
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