Physics · Optics

Refraction / Snell's Law

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What you learned

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Read next: Dispersion / Refractive Index and ColorColor changes n and bend

Key takeaway

Use refractive index as the speed clue: larger n means slower light.
Measure both angles from the normal before applying Snell's law.
Predict bend direction from whether the second medium is slower or faster.
Treat the critical angle as the point where the transmitted-angle solution stops being real.

Common misconception

Do not measure ray angles from the surface, and do not treat the boundary as a sideways push; the bend follows from speed change plus Snell's law.

The direction change comes from the speed difference between the two media, not from a separate sideways force at the boundary.

Keep this idea moving

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Color-dependent bendingOptics

Dispersion / Refractive Index and Color

Use one compact thin-prism bench to see how refractive index can depend on wavelength, why different colors bend by different amounts, and how a bounded prism model separates colors without widening into a full spectroscopy subsystem.

Critical-angle limitOptics

Total Internal Reflection

Push a ray from a higher-index medium toward a lower-index boundary, watch the critical angle emerge, and see the same live diagram hand off from ordinary refraction to full internal reflection.

Wave spreading linkOptics

Diffraction

Watch a wave spread after one narrow opening, see why diffraction grows when wavelength competes with slit width, and build the wave-optics bridge toward double-slit interference.

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Equation snapshotIndex and speed · Snell's lawShow 3 equations

Start with index as the speed clue, then use Snell's law for the angle; only use the critical-angle rule when light is leaving the higher-index side.

Index and speed
$n = \frac{c}{v}$
A larger refractive index means a smaller light speed in that medium.
Snell's law
$n_{1} sin (θ_{1}) = n_{2} sin (θ_{2})$
Relates the incident and transmitted angles for the same boundary. The same law handles bending toward the normal, bending away from it, and the approach to the critical-angle limit.
Critical angle
$sin (θ_{c}) = \frac{n _{2}}{n _{1}} (n_{1} > n_{2})$
This threshold exists only when light goes from higher n to lower n. At the threshold, the transmitted ray would run along the boundary at 90 degrees from the normal.

Key ideas

01A higher refractive index means a lower light speed in that medium.

02If the second medium is slower, the ray bends toward the normal. If the second medium is faster, it bends away.

03Snell's law, n_1 sin(theta_1) = n_2 sin(theta_2), lets you calculate the bend instead of guessing from a sketch.

04At normal incidence the speed can still change even when the direction does not, and if light goes from higher n to lower n above the critical angle, no real transmitted ray exists.

Worked examples

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Frozen walkthrough

These examples use the live incident angle and refractive indices from the stage, so each algebra step matches the ray you are actually watching.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current interface, what transmitted angle does Snell's law predict?

θ_{1}

Incident angle

50 °

n_{1}

Top-medium index

n_{2}

Bottom-medium index

1.5

1. Start with Snell's law

Use

n_{1} sin (θ_{1}) = n_{2} sin (θ_{2})

2. Solve for the transmitted sine

sin (θ_{2}) = \frac{n _{1}}{n _{2}} sin (θ_{1}) = \frac{1}{1.5} sin (5 0^{\circ}) = 0.51

3. Decide whether a real transmitted angle exists

θ_{2} = sin^{- 1} (0.51) = 30.7 1^{\circ}

Transmitted-angle result

θ_{2} = 30.7 1^{\circ}

The lower medium is slower, so the transmitted angle is smaller and the ray bends toward the normal.

Common misconception

Use this only when you want to pressure-test a mistaken intuition.

The boundary bends the ray by giving the light a sideways push.

The direction change comes from the speed difference between the two media, not from a separate sideways force at the boundary.

That is why the speed can change without a bend at normal incidence, and why changing the index contrast changes the bend even when the boundary itself does not move.

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