💡 Refraction
Snell's law: n₁ sin i = n₂ sin r. Apparent depth (object in denser medium): d' = d/n. Shift due to slab: t(1 − 1/n). Lateral shift: t sin(i−r)/cos r. Critical angle (denser → rarer): sin C = 1/n; for i > C, total internal reflection (TIR).
Refraction calculators
Snell, apparent depth, slab, lateral shift, critical angle
Solve for
n₂ (refractive index 2)
Angle of incidence i (°)
n₁ (refractive index 1)
Result
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Real depth d
Refractive index n (denser medium)
Apparent depth d' = d/n
—
Thickness t
Refractive index n
Shift = t(1 − 1/n)
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Thickness t
cm
Angle of incidence i (°)
Refractive index n
Lateral shift
—
Refractive index n (denser medium)
Critical angle C (denser → air)
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💧 Ray diagram
🧮Step-by-Step Solution▼ Show
| Concept | Formula | Notes |
|---|---|---|
| Snell's law | n₁ sin i = n₂ sin r | sin i / sin r = n₂/n₁ |
| Absolute refractive index | n = c / v | c = speed in vacuum |
| Apparent depth | d' = d / n | Object in denser medium viewed from rarer |
| Shift due to slab | Shift = t (1 − 1/n) | t = thickness |
| Lateral shift | d = t sin(i − r) / cos r | — |
| Critical angle | sin C = 1/n | Denser to rarer (n₂ = 1). TIR when i > C |
About refraction
Snell's law n₁ sin i = n₂ sin r relates angles of incidence and refraction at an interface. Apparent depth d' = d/n when viewing an object in a denser medium from air. A parallel slab shifts the ray by t(1 − 1/n) (normal shift) or laterally by t sin(i−r)/cos r. When light travels from denser to rarer medium, the critical angle satisfies sin C = 1/n; for angles of incidence greater than C, total internal reflection (TIR) occurs.