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All angles are measured from the normal, the dashed line at 90° to the surface. Drag the laser on the picture or use the slider. Never look into a real laser beam or shine one at people.
Reflection is light bouncing off a surface: the angle of reflection equals the angle of incidence, both measured from the normal. Refraction is light bending as it passes into a new material, because its speed changes. Light slows down in water (n = 1.33) and glass (n ≈ 1.5), so it bends toward the normal going in.
| Material | Refractive index n | Speed of light | Critical angle (to air) |
|---|---|---|---|
| Vacuum / air | 1.00 | 3.00 × 108 m/s | – |
| Water | 1.33 | 2.26 × 108 m/s | 48.8° |
| Perspex (acrylic) | 1.49 | 2.01 × 108 m/s | 42.2° |
| Crown glass | about 1.52 | 1.97 × 108 m/s | 41.1° |
| Diamond | 2.42 | 1.24 × 108 m/s | 24.4° |
| Where you meet it | What the light does |
|---|---|
| Mirrors, periscopes, bike reflectors | Reflection from smooth surfaces |
| Glasses, cameras, microscopes, your eye | Refraction by curved lenses |
| Optical fibers, endoscopes | Total internal reflection inside thin glass |
| Diamonds and cut glass | Total internal reflection plus dispersion: sparkle and “fire” |
| Rainbows | Refraction, reflection inside raindrops and dispersion |
| Mirages | Gradual refraction through hot air near the ground |
Move the object and change the focal length. Three standard rays find the image: a ray parallel to the axis, a ray through the center, and a ray through (or aimed at) the focal point. Dashed lines show where light only seems to come from (a virtual image).
F = focal point, 2F = twice the focal length, C = center of curvature of the mirror (at 2F). Heights are not to the same scale as distances.
Grades 6–8 only need the ideas above. This part is for high school (NGSS HS-PS4-1) and for anyone who wants the math.
Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, with n = c / v. Example: air into glass at 40°: sin θ₂ = sin 40° / 1.50 = 0.4285, so θ₂ = 25.4° (the glass block shows the same).
Critical angle (light going into air): sin c = 1 / n. Water: c = 48.8°; glass (1.50): 41.8°; diamond: 24.4°. Total internal reflection needs two things: light going into a material with a smaller n, and an angle bigger than c.
Why light bends: a wavefront that hits the surface at an angle has one edge enter the slower material first. That edge travels a shorter distance in the same time, so the wavefront swings round. The geometry gives sin θ₁ / v₁ = sin θ₂ / v₂, which is Snell’s law. The frequency (the color) never changes at a boundary; the speed and the wavelength do (λ = λ₀ / n).
How much is reflected: the Fresnel equations give the reflected share. For glass (1.50) it is 4 % head-on, 5 % at 40° and 39 % at 80°; beyond the critical angle it is 100 %. The simulator uses them for the brightness of every beam.
Thin lens and curved mirror: 1/f = 1/u + 1/v (real is positive), magnification m = −v / u, power P = 1/f in diopters (f in meters). A diverging lens or a convex mirror has a negative f. Convex lens, f = 10 cm, u = 30 cm: 1/v = 1/10 − 1/30, v = 15.0 cm, m = −0.50 (real, inverted, diminished).
Model notes: the simulator rounds glass to n = 1.50 and draws the prism’s color fan 3 times wider than real crown glass makes it (n = 1.514 red to 1.530 violet; the readouts use the real values). The optical fiber is a 7 mm glass light pipe in air seen in 2D; real fibers are thinner than a hair and have a cladding. The light pulses are slowed down about 15 billion times.
Name the parts of the classic ray-box experiment: light passing through a glass block (n = 1.50, 40°). Drag each word onto its numbered box, or tap a word and then tap the box. Press Check to see what is right. Tap a filled box to take the word back.
Tap a card, then tap the box it belongs in. Press Check when all 12 are placed.
Pick one answer for each question, then press Check my answers to see the explanations. New questions picks another set.
A 45-minute lesson. Open Laser in water on a projector (Full screen button) and ask the class to predict what happens when the laser under water is tilted more and more. Then let pairs do the six missions (each asks for a prediction before the bench shows the result; a certificate prints when all six are done) and the Ray Diagram Lab.
The angles follow the law of reflection and Snell’s law; the brightness of every beam follows the Fresnel equations; the critical angles are real. Glass is rounded to n = 1.50 (crown glass is about 1.52), the prism’s color fan is drawn 3 times wider than real (the readouts use the real values), and the optical fiber is a 7 mm glass light pipe in 2D (real fibers are thinner than a hair and have a cladding). The light pulses are slowed down about 15 billion times. Safety for hands-on work: never look into a real laser beam or point one at people; use a ray box or a low-power class 1/2 pointer.
Grades 6–8 stay qualitative (toward or away from the normal, and why). Go deeper has Snell’s law, the critical-angle formula, n = c / v, the lens equation and calculators for high school.
Standards: NGSS MS-PS4-2 (waves are reflected, absorbed or transmitted; the ray model of light) · high school: HS-PS4-1 (v = c / n, wavelength in a material) in Go deeper
| Time | Step | What students do | Go to |
|---|---|---|---|
| 5 min | Hook | Laser in water: predict, then tilt past 49° (mission 1) | Simulator |
| 10 min | Explore | Missions 2–4: mirror, glass block, straight on | Simulator |
| 8 min | Apply | Missions 5–6: prism colors, bending the fiber | Simulator |
| 10 min | Lenses | Ray Diagram Lab: convex lens at u = 30, 15 and 5 cm | Ray Diagram Lab |
| 5 min | Practice | Which way will the light bend? (6 rounds) | Prediction game |
| 7 min | Check | Quiz (10 questions) or the sort as an exit ticket | Quiz |
Worksheet: a print-out for students and a separate answer key page for the teacher (opens the print dialog; choose "Save as PDF" to keep a file).
When light reflects from a surface, the angle of incidence equals the angle of reflection. Both angles are measured from the normal, the imaginary line at 90° to the surface where the light hits it, and the incoming ray, the reflected ray and the normal all lie in the same plane. It works for any smooth surface, flat or curved.
Key takeaway: angle of incidence = angle of reflection.Light travels more slowly in water and glass than in air. When a beam hits the surface at an angle, one side of it enters and slows down first, so the beam swings round and changes direction. Going into a slower material it bends toward the normal; coming out into a faster one it bends away from the normal. Along the normal it slows down but does not bend.
Key takeaway: a change of speed at an angle makes light bend.The refractive index n tells you how much a material slows light down: n = speed of light in a vacuum ÷ speed in the material. Air is about 1.00, water 1.33, glass about 1.5 and diamond 2.42. The bigger the difference in n between two materials, the more light bends between them. Snell’s law links the angles: n₁ sin θ₁ = n₂ sin θ₂.
Key takeaway: n = c ÷ v.In reflection light bounces back off a surface into the same material, like your image in a mirror. In refraction light passes into a new material and bends because its speed changes, like a straw that looks bent in water. At most glass or water surfaces both happen at once: most light goes through and a little is reflected.
Key takeaway: reflection bounces; refraction bends.When light goes from a slower material into a faster one, such as water into air, it bends away from the normal. At the critical angle the outgoing ray skims along the surface, and at any bigger angle no light can get out at all: all of it reflects back inside. The critical angle is about 49° for water, 42° for glass and only 24° for diamond.
Key takeaway: beyond the critical angle, all the light reflects inside.An optical fiber is a thin strand of very clear glass. Light inside keeps hitting the wall at more than the critical angle, so it is totally reflected again and again and follows the fiber, even around gentle bends. If the fiber is bent too sharply, the light meets the wall at a smaller angle and some leaks out. Fibers carry internet and phone signals as flashes of light.
Key takeaway: total internal reflection keeps the light inside.Light from the underwater part bends away from the normal as it leaves the water. Your brain assumes light travels in straight lines, so it traces the rays back to a point higher than the real one. Looking straight down, the apparent depth is the real depth divided by the refractive index: a 2 m pool looks about 1.5 m deep.
Key takeaway: apparent depth = real depth ÷ n.White light is a mixture of all the colors. Glass slows violet light slightly more than red light, so violet has a slightly bigger refractive index and bends more. Passing through the two slanted faces of a prism, the colors fan out into a spectrum: red, orange, yellow, green, blue and violet. This is called dispersion; raindrops do the same to make a rainbow.
Key takeaway: each color bends by a different amount.A convex lens is thicker in the middle. It converges light: parallel rays meet at the focal point, and it can make real images on a screen (cameras, projectors, your eye) or act as a magnifying glass. A concave lens is thinner in the middle. It diverges light, so it always makes a smaller, upright, virtual image; glasses for nearsighted people use concave lenses.
Key takeaway: convex converges; concave diverges.A real image forms where light rays actually meet, so it can be caught on a screen, like the picture from a projector; for a single lens or mirror it is upside down. A virtual image is where the rays only seem to come from, like your reflection in a mirror or the view through a magnifying glass; it cannot be put on a screen.
Key takeaway: real images can go on a screen; virtual ones cannot.Yes for the physics: the angles follow the law of reflection and Snell’s law, the share of light reflected at each surface follows the Fresnel equations, the critical angles are real and the prism uses a real formula for how the refractive index of glass changes with color. The simplifications: glass is rounded to n = 1.50, the color fan of the prism is drawn 3 times wider than real glass makes it (the readouts use the real values), the fiber is a thick 2D light pipe, and the light pulses are slowed down about 15 billion times.
Key takeaway: real laws and numbers, simplified pictures.