Determine Critical Angle and Refractive Index of Water
✅ FREE Experiment • 🌊 Interactive Ray Tracing • 🎓 NEB Class 12 Physics
When light travels from a denser medium (like water) to a rarer medium (like air), it bends away from the normal. As the angle of incidence increases, the angle of refraction also increases. At a particular angle of incidence called the critical angle (θc), the refracted ray grazes along the interface (refraction angle = 90°). Beyond this critical angle, refraction is not possible, and the light is completely reflected back into the denser medium - a phenomenon called Total Internal Reflection (TIR).
In this experiment, we determine the critical angle of water by observing when TIR occurs. The critical angle is related to refractive index by: sin(θc) = 1/n, where n is the refractive index of water with respect to air. By measuring θc, we can calculate the refractive index of water.
Angle from the normal inside water
n = 1.33 for pure water at 20°C
💡 Tip: Gradually increase the incident angle. At the critical angle, the refracted ray will graze along the water-air interface (r = 90°). Beyond this, you'll observe total internal reflection!
Where n₁ = refractive index of denser medium (water), n₂ = refractive index of rarer medium (air ≈ 1)
Given: Refractive index of air nair = 1.00
| S.No. | Incident Angle i (degrees) |
Refracted Angle r (degrees) |
sin(i) | sin(r) | Observation | Critical Angle θc (degrees) |
n = 1/sin(θc) |
|---|---|---|---|---|---|---|---|
|
No observations recorded yet. Adjust angle and click "Record" to add readings. Try different angles from 0° to 90° to observe refraction → critical angle → TIR |
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Mean Refractive Index of Water: Calculate after recording observations near critical angle
When light passes from one transparent medium to another, it changes direction at the interface. This bending of light is called refraction. The relationship between angles of incidence (i) and refraction (r) is given by Snell's Law:
Where n₁ and n₂ are refractive indices of the two media.
When light travels from a denser medium (higher refractive index) to a rarer medium (lower refractive index), the refracted ray bends away from the normal. As the angle of incidence increases, the angle of refraction also increases. The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is exactly 90° (ray grazes along the interface).
At critical angle θc, the refracted angle r = 90°:
n₁ = nwater ≈ 1.33 (denser medium)
n₂ = nair ≈ 1.00 (rarer medium)
For water, θc ≈ 48.6°, giving n ≈ 1.33
When the angle of incidence exceeds the critical angle (i > θc), refraction is not possible. All the light is reflected back into the denser medium. This phenomenon is called Total Internal Reflection.
When incident angle is less than critical angle, light refracts into air. As i increases, the refracted ray bends more away from normal, and r increases.
At exactly the critical angle, the refracted ray grazes along the interface (r = 90°). This is the boundary condition between refraction and total internal reflection.
Beyond critical angle, refraction is impossible. All light reflects back into water, following the law of reflection.
| Medium | Refractive Index (n) | Critical Angle (with air) |
|---|---|---|
| Air | 1.00 | - |
| Water | 1.33 | 48.6° |
| Glass (crown) | 1.52 | 41.1° |
| Diamond | 2.42 | 24.4° |
Critical angle is the angle of incidence in a denser medium for which the angle of refraction in a rarer medium is exactly 90° (refracted ray grazes along the interface). It's denoted by θc. For angles greater than θc, total internal reflection occurs.
Total Internal Reflection (TIR) is the phenomenon where all incident light is reflected back into the denser medium when: (1) light travels from denser to rarer medium, and (2) angle of incidence exceeds the critical angle. In TIR, 100% of light is reflected with no transmission into the rarer medium.
At critical angle θc, refracted angle r = 90°.
By Snell's law: n₁ sin(θc) = n₂ sin(90°)
n₁ sin(θc) = n₂ × 1
sin(θc) = n₂/n₁
For water-air interface: n₁ = nwater, n₂ = nair = 1
Therefore: sin(θc) = 1/nwater
Or: nwater = 1/sin(θc)
Two conditions are necessary:
1. Medium condition: Light must travel from denser medium to rarer medium
(higher to lower refractive index, n₁ > n₂)
2. Angle condition: Angle of incidence must be greater than the critical
angle (i > θc)
If either condition is not satisfied, TIR will not occur.
When light goes from denser to rarer medium, it bends away from normal (r > i). As i increases, r increases faster and can reach 90° at critical angle. Beyond this, refraction is geometrically impossible (r cannot exceed 90°), so TIR occurs. When light goes from rarer to denser, it bends toward normal (r < i), so r can never reach 90°, making TIR impossible.
The critical angle for water (with respect to air) is approximately 48.6° or 48°35'. This is calculated using: sin(θc) = 1/n = 1/1.33 ≈ 0.752, therefore θc = sin⁻¹(0.752) ≈ 48.6°. This means for angles greater than 48.6°, total internal reflection occurs at the water-air interface.
Optical fibers consist of a core (high refractive index glass) surrounded by cladding (lower refractive index). Light entering at one end undergoes multiple total internal reflections at the core-cladding interface as it travels along the fiber. Since TIR is 100% efficient (no light loss), signals can travel long distances without significant attenuation. This enables high-speed internet and telecommunications.
Diamond has a very high refractive index (n = 2.42), giving it a low critical angle (24.4°). When light enters a cut diamond, it undergoes multiple total internal reflections before exiting. The specific cut maximizes these reflections. Combined with high dispersion (splitting white light into colors), this creates the characteristic sparkle and "fire" of diamonds.
A mirage is an optical illusion where distant objects appear inverted or shimmering, often with an appearance of water on hot roads. It occurs because hot air near the ground has lower refractive index than cooler air above. Light from sky/objects bends away from normal as it enters progressively less dense air. Eventually it undergoes TIR, making it appear as if reflected from water surface.
Yes, but only within a specific cone called "Snell's window". Due to refraction and the critical angle of water (48.6°), a fish can see the entire above-water world compressed into a cone of angle 2×48.6° = 97.2°. Outside this cone, the fish sees only reflected images of underwater objects due to TIR. You appear highly compressed near the edge of this circle.
TIR advantages over mirrors:
1. 100% reflection efficiency (no light loss), mirrors lose ~4%
2. No deterioration - glass/water interface doesn't degrade
3. No silvering needed - cheaper in some applications
4. Multiple reflections don't accumulate losses
5. Works for any wavelength uniformly
This makes TIR ideal for binoculars, periscopes, and fiber optics.
At exactly the critical angle (i = θc), the refracted ray grazes along the interface between the two media (r = 90°). The ray travels parallel to the boundary surface. This is the transition point: below θc there's refraction, at θc the ray grazes, and above θc there's total internal reflection.
Yes! Refractive index varies slightly with wavelength (dispersion). Since sin(θc) = 1/n, critical angle also depends on color. Red light has slightly lower n, so higher critical angle. Violet has higher n, so lower critical angle. This difference is small (~1-2°) but observable in precise experiments. It's the basis of how prisms separate colors.
Regular Reflection: Occurs at any interface, any medium, any angle. Only part
of light reflects (~4% for glass-air), rest is transmitted. Surface quality matters.
Total Internal Reflection: Occurs only from denser to rarer medium, only when
i > θc. 100% of light reflects, nothing is transmitted. Surface quality less critical
since reflection occurs at interface, not surface coating.
Method: Use a semicircular glass/water container. Send light from curved side (no refraction at entry). Gradually increase angle of incidence at the flat surface. Observe refracted ray bending more and more. At critical angle, refracted ray becomes parallel to interface (r = 90°). Measure this angle carefully. Beyond it, observe total internal reflection. Take multiple readings near critical angle and find mean for accuracy.