Refraction of light

1. Overview

Refraction is the change in direction of a light ray when it passes from one transparent medium to another, such as from air into glass. This occurs because light changes speed when it enters a material of different optical density, a fundamental principle that allows lenses, cameras, and the human eye to function.

Key Definitions

• Normal: An imaginary line drawn at 90° (perpendicular) to the surface where the light ray hits the boundary.
• Angle of Incidence ($i$): The angle between the incident (incoming) ray and the normal.
• Angle of Refraction ($r$): The angle between the refracted ray and the normal.
• Critical Angle ($c$): The specific angle of incidence that results in an angle of refraction of 90°, where the light travels along the boundary.
• Total Internal Reflection (TIR): When light traveling from a denser medium hits a boundary at an angle greater than the critical angle, and all light is reflected back into the medium.
• Refractive Index ($n$): A measure of how much a medium slows down the speed of light.

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Core Content

The Passage of Light Through Boundaries

When light travels between two different mediums:

• Air to Glass (Less dense to more dense): Light slows down and bends towards the normal. ($i > r$)
• Glass to Air (More dense to less dense): Light speeds up and bends away from the normal. ($r > i$)
• Along the Normal: If light enters at 90° to the surface, its speed changes but its direction does not.

Experiment: Investigating Refraction

1. Place a transparent rectangular block on a piece of paper and trace its outline.
2. Shine a thin beam of light (from a ray box) into the side of the block at an angle.
3. Mark the path of the incident ray and the emergent ray with dots.
4. Remove the block, connect the dots, and draw the path of the ray inside the block.
5. Draw a normal at the point of entry and use a protractor to measure the angle of incidence ($i$) and angle of refraction ($r$).
6. Repeat for different shapes like semi-circular blocks to observe the critical angle.

Internal Reflection and Total Internal Reflection (TIR)

This occurs only when light moves from a more dense medium (glass/water) toward a less dense medium (air).

1. Angle $i <$ Critical Angle: Most light refracts out, some reflects internally.
2. Angle $i =$ Critical Angle: The refracted ray travels at 90° along the boundary.
3. Angle $i >$ Critical Angle: Total Internal Reflection occurs; no light escapes.

Everyday Examples:

• Prisms in Binoculars: Use TIR to turn light 180° to shorten the length of the device.
• Diamonds: The sparkle is caused by multiple internal reflections due to a very small critical angle.

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Extended Content (Extended Only)

The Refractive Index ($n$)

The refractive index is a ratio that describes the optical density of a material. It has no units.

1. Using Speeds: $$n = \frac{\text{speed of light in medium 1}}{\text{speed of light in medium 2}}$$ (Usually, medium 1 is a vacuum or air, where light is fastest).

2. Using Snell’s Law: For light entering a medium from air: $$n = \frac{\sin(i)}{\sin(r)}$$

3. Using the Critical Angle: When the angle of refraction is 90°: $$n = \frac{1}{\sin(c)}$$

Worked Example:

A ray of light hits a glass block with an angle of incidence of 45°. If the refractive index of glass is 1.5, calculate the angle of refraction.

1. $n = \sin(i) / \sin(r)$
2. $1.5 = \sin(45) / \sin(r)$
3. $\sin(r) = \sin(45) / 1.5 = 0.707 / 1.5 = 0.471$
4. $r = \sin^{-1}(0.471) = 28.1^\circ$

Optical Fibres

Optical fibres are thin strands of glass or plastic that use Total Internal Reflection to transmit pulses of light over long distances.

• Telecommunications: Light pulses carry data (internet, phone signals) much faster and with less signal loss than copper wires.
• Medicine: Used in endoscopes to see inside the human body.

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Key Equations

Equation	Symbols	Units
$n = \frac{\sin i}{\sin r}$	$n$ = Refractive index, $i$ = incidence, $r$ = refraction	$n$ (None), $i/r$ (degrees)
$n = \frac{v_1}{v_2}$	$v_1$ = Speed in air, $v_2$ = Speed in medium	$v$ (m/s)
$n = \frac{1}{\sin c}$	$c$ = Critical angle	$c$ (degrees)

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Common Mistakes to Avoid

• ❌ Wrong: Measuring the angle between the ray and the surface of the block.
  • ✓ Right: Always measure the angle between the ray and the normal.
• ❌ Wrong: Showing light bending away from the normal when entering a denser medium (like glass).
  • ✓ Right: Remember "FAST" (Faster Away, Slower Towards). Light slows down in glass, so it moves towards the normal.
• ❌ Wrong: Drawing the light ray going straight through at an angle without bending.
  • ✓ Right: Light must change direction unless it enters exactly along the normal (0°).
• ❌ Wrong: Assuming TIR can happen when light goes from air into glass.
  • ✓ Right: TIR only happens when light tries to leave a denser medium to enter a less dense one.

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Exam Tips

1. The "Normal" is Priority: In any refraction diagram, draw the normal dashed line first. It is the reference point for all angles.
2. Check your Calculator: Ensure your calculator is in DEG (Degrees) mode, not RAD (Radians), before calculating sines.
3. Emergent Ray Parallelism: If a ray enters and leaves a rectangular block, the final emergent ray should be drawn parallel to the original incident ray.