Ray Optics Fundamentals
Refraction of Light
Discover how light waves bend and change speeds when crossing optical boundaries. Cycle through a realistic glass of water holding a bent pencil, a lab laser beam passing through a glass block, and a sunny swimming pool showing apparent depth displacement.
Light Refraction virtual workbench
Animate real-world setups to explore optical density, speed changes, and spatial displacement.
Live Telemetry
Snell's Law: n₁ sin i = n₂ sin r- Medium 1 (n₁)
- Air (1.00)
- Medium 2 (n₂)
- Water (1.33)
- Incident Angle (i)
- 45.0°
- Refraction Angle (r)
- 32.0°
- Light Speed Change
- Slower (0.75c)
- Wavelength Change
- Compressed (0.75λ)
Understanding the Refraction of Light
**Refraction** is the bending of a light ray as it crosses the boundary between two optical media with different refractive properties. This optical bending is an direct consequence of the speed of light changing as it crosses the interface.
The Physical Cause: Changes in Wave Speed
Although light is the fastest entity in the universe, it only travels at its absolute speed ($c \approx 3.00 \times 10^8$ m/s) inside a vacuum. When passing through material particles (like glass or water), light interacts with the electrons of the material, slowing its net propagation speed.
- When light travels from an **optically rarer medium** (faster speed, lower $n$) into an **optically denser medium** (slower speed, higher $n$), the light wave front slows down unevenly, causing the ray to bend **toward the normal** ($r < i$).
- When light travels from an **optically denser medium** into an **optically rarer medium**, the wave front speeds up, bending the ray **away from the normal** ($r > i$).
Snell's Law of Refraction
The mathematical relationship governing the direction change is known as **Snell's Law** (or the Second Law of Refraction):
Where:
- **$n_1$**: Refractive index of the first medium (where the incident ray travels).
- **$n_2$**: Refractive index of the second medium (where the refracted ray travels).
- **$i$**: The **angle of incidence** (angle between the incident ray and the perpendicular normal line).
- **$r$**: The **angle of refraction** (angle between the refracted ray and the normal).
Refractive Index ($n$)
The **refractive index** (also called index of refraction) measures a medium's optical density. It represents the ratio of the speed of light in a vacuum ($c$) to its speed inside the medium ($v$):
Since $v$ is always less than or equal to $c$, the refractive index $n$ is always greater than or equal to 1.0. For example, $n_{\text{air}} \approx 1.00$, $n_{\text{water}} \approx 1.33$, and $n_{\text{glass}} \approx 1.50$.
Apparent Depth and Displacement
Refraction causes objects submerged in water or placed behind glass blocks to appear spatially shifted. When viewing a submerged object from air, light rays travel from water (denser) to air (rarer), bending away from the normal at the surface.
The observer's brain traces these incoming rays straight back, projecting a shallower **virtual image** closer to the surface. For vertical viewing, the relationship between actual depth ($d$) and apparent depth ($d'$) is:
This explains why swimming pools appear shallower than their physical depth, and why coins placed in a cup seem to float upward when water is added.
Solved Examples
Example 1
A ray of light in air strikes a glass block at an angle of incidence of 45.0 degrees. If the refractive index of the glass is 1.50, calculate the angle of refraction.
View Step-by-Step Solution
- Identify values: Medium 1 is air, so n_1 = 1.00. Medium 2 is glass, so n_2 = 1.50. The angle of incidence i = 45.0 degrees.
- Recall Snell's Law: n_1 * sin(i) = n_2 * sin(r).
- Rearrange the formula to solve for sin(r): sin(r) = (n_1 * sin(i)) / n_2.
- Substitute values: sin(r) = (1.00 * sin(45.0 degrees)) / 1.50 = (1.00 * 0.7071) / 1.50 = 0.4714.
- Find the inverse sine: r = arcsin(0.4714) ≈ 28.1 degrees.
- Since glass is optically denser than air (n_2 > n_1), the light bends toward the normal, resulting in a smaller angle (28.1 degrees < 45.0 degrees).
Final Answer: Angle of Refraction = 28.1 degrees.
Example 2
Calculate the speed of light in water if the refractive index of water is 1.33. The speed of light in a vacuum is 3.00 * 10^8 m/s.
View Step-by-Step Solution
- Identify values: Refractive index of water n = 1.33, speed of light in vacuum c = 3.00 * 10^8 m/s.
- Use the definition of refractive index: n = c / v, where v is the speed of light in the medium.
- Rearrange the equation to solve for v: v = c / n.
- Substitute the values: v = (3.00 * 10^8 m/s) / 1.33 ≈ 2.26 * 10^8 m/s.
- This shows light travels significantly slower in water than in a vacuum.
Final Answer: Speed of Light in Water ≈ 2.26 * 10^8 m/s.
Example 3
A swimming pool is filled with water of refractive index 1.33. A coin lying at the bottom of the pool appears to be at a depth of 3.00 m when viewed from directly above. What is the actual depth of the pool?
View Step-by-Step Solution
- Identify values: Refractive index of water n = 1.33. Apparent depth d' = 3.00 m.
- Recall the apparent depth formula: Apparent Depth = Actual Depth / Refractive Index (d' = d / n).
- Rearrange to solve for actual depth: d = d' * n.
- Substitute values: d = 3.00 m * 1.333 ≈ 4.00 m.
- The pool is actually 4.00 m deep, but refraction makes it look shallower.
Final Answer: Actual Depth of the Pool = 4.00 m.
Self-Check Questions
Question 1
Why does the frequency of light remain unchanged during refraction?
Show Answer & Explanation
Frequency is a fundamental property of the light source (determined by the oscillations of electrons generating the wave). When light enters a new medium, the speed and wavelength change proportionally (v = f * λ), but the rate at which wave crests pass a boundary remains the same, leaving the frequency constant.
Question 2
Explain the physical meaning of a refractive index of 2.42 for a diamond.
Show Answer & Explanation
A refractive index of 2.42 means that: (1) Light travels 2.42 times slower in a diamond than in a vacuum. (2) When light enters a diamond from air, it bends sharply toward the normal. This high optical density leads to a very small critical angle, trapping light inside and causing the diamond's signature sparkle.
Question 3
Under what two conditions does light NOT bend when crossing a boundary?
Show Answer & Explanation
Light will cross a boundary without bending if: (1) The angle of incidence is exactly 0 degrees (normal incidence), meaning the light strikes the interface perpendicularly. (2) The two media have identical refractive indices (n_1 = n_2), meaning there is no change in the speed of light.
Question 4
Why does a swimming pool look shallower than it actually is when viewed at an angle?
Show Answer & Explanation
Light rays coming from the bottom of the pool travel from water (denser) to air (rarer) and bend away from the normal at the surface. When these refracted rays reach the observer's eye, the brain traces them backward along straight lines. These virtual lines intersect at a shallower location, projecting a virtual image of the pool floor higher up.