← Optics 1

Optics tools

Standalone sandboxes from the lectures, for homework and exploring.

Snell’s Law Lab

Pick two media and drag the ray to see refraction and total internal reflection.

Refraction from Air into WaterAirn₁ = 1.000Watern₂ = 1.333normalθ₁ 40.0°θ₂ 28.8°
n1 sin θ1 = n2 sin θ2
1.000 × sin 40.0° = 1.333 × sin 28.8°(both sides = 0.643)

Lens Bench

Set the lens power and the vergence of the incoming light. V = U + P.

Optical bench: light passing through a thin lens−40−30−20−100+10+20+30+40cm+5.00 DF′Ff = 20.0 cm
Incoming U0.00collimated
Lens P+5.00diopters
Outgoing V+5.00converging
Focal length+20.0 cmf = 1/P
U+P=V  ⇒  (0.00)+(+5.00)=+5.00 DU + P = V \;\Rightarrow\; (0.00) + (+5.00) = +5.00\,\text{D}
Set the incoming vergence U and the lens power P. The lens adds its power: V=U+PV = U + P. Positive V converges to a real point at 1/V; negative V diverges from a virtual one.

Vergence Meter

Move the observer to see how vergence changes with distance.

Vergence at 4.0 m: −0.25 Dsource1 cm10 cm1 m10 md = 4.0 mdistance (log scale)Wavefront at the eyedashed = flat (0 D)
V=−1d=−14.00 m=−0.25 DV = -\frac{1}{d} = -\frac{1}{4.00\,\text{m}} = -0.25\,\text{D}
Vergence−0.25 D
Light is
Vergence is the reciprocal of the distance (in meters) to the point light is diverging from or converging to. Closer to the point means more curved wavefronts and larger vergence.

Mirror Sandbox

Angles of incidence and reflection, from the normal or the surface.

Reflection of a light ray off a flat mirrornormalmirror surfaceθᵢ 35°θᵣ 35°55°55°
Measure from
θ incidence35°
θ reflection35°
Drag the light source. The angle of reflection always equals the angle of incidence, both measured from the normal.

Lens Thickness

Compare lens materials for the same prescription.

Lens thickness for a −6.00 D lens in four materialsCR-39n = 1.498edge 7.1 mmreference (thickest)Polycarbonaten = 1.586edge 6.2 mm13% thinnerHigh-index 1.67n = 1.670edge 5.6 mm21% thinnerHigh-index 1.74n = 1.740edge 5.2 mm27% thinner
Same −6.00 D prescription, 60 mm lens, drawn to scale. A higher index needs less curvature for the same power, so the lens is thinner.