Refraction of light Revision Notes

The normal line is an imaginary line drawn perpendicular (at 90°) to the surface at the exact point where a light ray strikes the boundary between two different media. It serves as a reference line from which angles are measured in refraction problems.

To construct the normal line in a ray diagram: first identify the point of incidence where the light ray meets the surface, then draw a straight line at right angles to the surface at that point. This line is the normal.

• The normal line is always perpendicular to the surface at the point of incidence.
• It is an imaginary reference line used to measure angles of incidence and refraction.

The angle of incidence is the angle between the incoming light ray (incident ray) and the normal line at the point of incidence.

It is measured in degrees (°) using a protractor placed at the point of incidence, with the zero line along the normal.

This angle quantifies how the light ray approaches the boundary between two media.

• Angle of incidence (i) is measured from the normal to the incident ray.
• Units of angle of incidence are degrees (°).

When light passes from one transparent medium into another (for example, from air into glass), it changes speed, causing the light ray to bend. This bending is called refraction.

The angle of refraction is the angle between the refracted ray (the ray inside the second medium) and the normal line at the point of incidence.

Like the angle of incidence, it is measured in degrees using a protractor at the point of incidence.

• Angle of refraction (r) is measured from the normal to the refracted ray.
• Units of angle of refraction are degrees (°).

Light changes direction at the boundary between two media because its speed changes. The speed of light is different in different materials due to their optical densities.

When light enters a denser medium (e.g., air to glass), it slows down and bends towards the normal.

When light enters a less dense medium (e.g., glass to air), it speeds up and bends away from the normal.

• Refraction occurs due to change in speed of light between media.
• Light bends towards the normal when entering a denser medium.
• Light bends away from the normal when entering a less dense medium.

To accurately represent refraction in a ray diagram:

1. Draw the boundary line between two media horizontally.

2. At the point where the incident ray meets the boundary, draw the normal line perpendicular to the boundary surface (90°). This is the reference line for measuring angles i and r. 3. Draw the incident ray approaching the boundary, making an angle i with the normal line. 4. Draw the refracted ray on the other side of the boundary, bending towards or away from the normal depending on the media, making an angle r with the normal. 5. Label the angles of incidence (i) and refraction (r) clearly between the rays and the normal line.

• Normal line is perpendicular to the boundary at the point of incidence.
• Angles i and r are measured from the normal to the respective rays.
• Refracted ray bends towards or away from the normal depending on media.

Refraction is the change in direction of a light ray when it passes from one transparent medium into another with a different optical density. This occurs because the speed of light changes between media. When light enters a denser medium (higher refractive index), it slows down and bends towards the normal line, an imaginary line perpendicular to the surface at the point of incidence. Conversely, when light passes into a less dense medium, it speeds up and bends away from the normal.

The angle of incidence (i) is the angle between the incident ray and the normal. The angle of refraction (r) is the angle between the refracted ray and the normal. Both angles are measured in degrees.

Refraction obeys Snell's Law: n₁ sin i = n₂ sin r, where n₁ and n₂ are the refractive indices of the first and second media respectively. Although this experiment focuses on observing refraction qualitatively, understanding these angles is essential for accurate measurement and interpretation.

• Refraction occurs due to change in light speed between media.
• Angle of incidence and refraction are measured relative to the normal.
• Light bends towards the normal entering a denser medium, away when entering a less dense medium.

To perform the refraction experiment, you will need:

• A ray box or laser pointer to produce a narrow, visible beam of light.
• Transparent blocks of various shapes, such as: rectangular prism, triangular prism, and semicircular block, made from materials like glass or acrylic.
• Protractor for measuring angles accurately.
• White paper or a drawing board to place under the blocks for marking rays.
• Pencil and ruler for drawing normal lines and ray paths.
• A stand or clamp to hold the light source steady (optional but recommended).

1. Place the white paper on a flat surface and position the transparent block on it.

2. Using a pencil and ruler, draw the outline of the block on the paper to keep it fixed during the experiment.

3. Draw a normal line perpendicular to the surface where the light will enter the block. This is usually done at the midpoint of one face of the block where the light will be incident. Mark this point clearly as the point of incidence (O).

• 4. Set up the ray box or laser pointer so that it emits a narrow beam of light directed at the point O on the block's surface at a known angle of incidence (for example, 30° to the normal).
• 5. Observe the path of the light as it enters the block. Mark the incident ray on the paper before the block and the refracted ray inside the block by placing dots along the beam path and connecting them with a ruler.
• 6. Measure the angle of incidence (i) between the incident ray and the normal line using the protractor.
• 7. Measure the angle of refraction (r) between the refracted ray inside the block and the normal line.
• 8. Repeat the measurements for different angles of incidence (e.g., 20°, 40°, 50°) to observe how the angle of refraction changes.
• 9. Repeat the entire procedure with different shaped blocks to observe how the shape affects the path of the refracted light.

To represent the experiment visually, draw ray diagrams following these steps:

• Draw the outline of the transparent block to scale.
• At the point of incidence on the surface, draw the normal line perpendicular to the surface.
• Draw the incident ray approaching the block at the measured angle of incidence to the normal.
• Inside the block, draw the refracted ray bending towards or away from the normal depending on the medium.
• Extend the refracted ray to the opposite side if the block is transparent on both sides.
• Label all angles clearly: angle of incidence (i) and angle of refraction (r).

Variables to control include the angle of incidence, the shape and material of the block, and the position of the light source. To improve accuracy:

• Use a narrow, well-defined light beam to clearly see refraction.
• Ensure the block is stable and does not move during measurements.
• Measure angles carefully using a protractor aligned with the normal line.
• Repeat measurements multiple times and calculate averages to reduce random errors.
• Use blocks made of materials with known refractive indices for comparison if desired.
• Safety precautions include avoiding direct eye exposure to the laser beam and handling glass blocks carefully to prevent breakage and injury.

Light travels in straight lines when it moves through a uniform transparent medium such as air, water, or glass. This straight-line travel is due to the wavefronts of light moving forward without obstruction or change in the medium's properties.

The speed of light in a vacuum is approximately 3.0 × 10⁸ m/s, but in transparent materials, light travels slower due to interactions with the material's atoms.

The speed of light in a medium is given by v = c/n, where c is the speed of light in vacuum and n is the refractive index of the medium (a dimensionless quantity greater than or equal to 1).

• Light speed in vacuum, c = 3.0 × 10⁸ m/s.
• Refractive index, n = c / v, where v is speed in the medium.
• Light travels in straight lines within a uniform medium.

When light passes from one transparent medium into another with a different refractive index, it encounters an interface. At this boundary, the speed of light changes, which causes the light to change direction, a process called refraction.

The interface is a flat or curved surface separating two materials, for example, air and glass or water and air.

The change in speed at the interface depends on the optical density of the materials, which is related to their refractive indices.

• Interface: boundary between two transparent media.
• Speed of light changes at the interface.
• Change in speed causes bending of light (refraction).

Refraction is the bending of light as it passes from one medium to another due to a change in its speed.

If light travels from a less optically dense medium (lower refractive index) to a more optically dense medium (higher refractive index), it slows down and bends towards the normal (an imaginary line perpendicular to the interface).

Conversely, if light travels from a more optically dense medium to a less optically dense medium, it speeds up and bends away from the normal.

• Refraction occurs at the interface due to speed change.
• Light bends towards the normal when entering a denser medium.
• Light bends away from the normal when entering a less dense medium.

The change in speed of light is caused by the interaction of the electromagnetic wave with the atoms in the medium, which absorb and re-emit the light, effectively slowing its progress.

Because the speed changes, the wavefronts change direction to maintain continuity across the boundary, resulting in bending of the light ray.

This bending is predictable and consistent, allowing the use of laws such as Snell's Law to quantify it (covered in other objectives).

• Light interacts with atoms, changing speed.
• Wavefront direction changes to maintain continuity.
• Refraction is a predictable bending of light.

To represent refraction, draw a straight line representing the interface between two media.

Draw the normal line perpendicular to the interface at the point where the light ray meets it.

Draw the incident ray approaching the interface at an angle to the normal (angle of incidence). Then draw the refracted ray bending towards or away from the normal depending on the relative refractive indices of the two media.

• Interface line separates two media.
• Normal line is perpendicular to interface.
• Incident ray and refracted ray angles show bending direction.

When light passes from one transparent medium to another, its speed changes, causing the light to change direction; this phenomenon is called refraction.

The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v): n = c/v.

Refractive indices are always greater than or equal to 1, with air approximately 1.00 and denser media like glass or water having higher values (e.g., glass ~1.5).

• Refraction occurs at the boundary between two media with different refractive indices.
• Light bends towards the normal when entering a denser medium (higher n).
• Light bends away from the normal when entering a less dense medium (lower n).

The critical angle is defined for light travelling from a denser medium to a less dense medium.

It is the minimum angle of incidence in the denser medium for which the angle of refraction in the less dense medium is 90°, meaning the refracted ray travels along the boundary.

At angles of incidence greater than the critical angle, no refraction occurs; instead, all the light is reflected back into the denser medium, a phenomenon called total internal reflection.

• Critical angle (θc) only exists when light moves from a medium with refractive index n₁ to one with refractive index n₂, where n₁ > n₂.
• At θ = θc, the refracted ray grazes the boundary (angle of refraction r = 90°).
• For θ > θc, total internal reflection occurs.

Using Snell's law: n₁ sin i = n₂ sin r, where i is the angle of incidence and r is the angle of refraction.

At the critical angle, i = θc and r = 90°, so sin r = sin 90° = 1.

Rearranging Snell's law gives the formula for the critical angle: sin θc = n₂ / n₁, where n₁ > n₂.

• Formula: sin θc = n₂ / n₁
• θc = sin⁻¹ (n₂ / n₁)
• Units: angles in degrees or radians; refractive indices are dimensionless.
• Example calculation: For light going from glass (n₁ = 1.5) to air (n₂ = 1.0), sin θc = 1.0 / 1.5 = 0.6667, so θc = sin⁻¹(0.6667) ≈ 41.8°.
• Common error: Mixing up n₁ and n₂ or applying the formula when n₂ > n₁ (no critical angle exists).

The critical angle arises because light bends away from the normal when moving to a less dense medium; beyond a certain angle, refraction cannot occur and light is reflected internally.

Total internal reflection is used in optical fibres to trap light within the core, allowing signals to travel long distances with minimal loss.

Other applications include prisms in binoculars and certain types of sensors.

• Total internal reflection occurs only if n₁ > n₂ and angle of incidence > θc.
• Optical fibres rely on total internal reflection to guide light efficiently.
• Understanding the critical angle helps explain phenomena like shimmering on hot roads and mirages.

To draw a ray diagram illustrating the critical angle:

1. Draw a horizontal boundary line separating two media, with the denser medium below and the less dense medium above.

2. Draw the normal line perpendicular to the boundary at the point of incidence (where the ray meets the boundary).

• 3. Draw an incident ray in the denser medium approaching the boundary at the critical angle θc to the normal.
• 4. Draw the refracted ray along the boundary line (at 90° to the normal) in the less dense medium.
• 5. Label the angles: angle of incidence θc in the denser medium, angle of refraction 90° in the less dense medium.
• 6. Indicate the refractive indices n₁ (denser medium) and n₂ (less dense medium).

Internal reflection occurs when light travelling within a denser medium (higher refractive index) strikes the boundary with a less dense medium (lower refractive index) and is reflected back into the denser medium rather than refracted out.

Total internal reflection (TIR) is a special case of internal reflection where all the incident light is reflected back into the denser medium, with no refraction into the less dense medium.

TIR only occurs when two conditions are met: (1) light travels from a denser to a less dense medium, and (2) the angle of incidence at the boundary is greater than the critical angle for those two media.

• Internal reflection: partial reflection of light inside a denser medium at the boundary with a less dense medium.
• Total internal reflection: complete reflection of light inside the denser medium when angle of incidence > critical angle.
• Light must travel from denser to less dense medium (e.g., glass to air) for TIR to occur.

The critical angle (c) is the minimum angle of incidence in the denser medium for which the angle of refraction in the less dense medium is 90°, meaning the refracted ray travels along the boundary.

For angles of incidence greater than the critical angle, refraction cannot occur and total internal reflection happens.

The critical angle is related to the refractive index (n) of the denser medium relative to the less dense medium by the formula: sin c = 1/n, assuming the less dense medium is air (refractive index ≈ 1).

• Critical angle (c): angle of incidence where refracted ray is at 90° to the normal.
• Formula: sin c = 1/n, where n = refractive index of denser medium relative to air.
• Refractive index n = speed of light in air / speed of light in medium (dimensionless).

When light passes from a denser medium (refractive index n) to air, the critical angle c is given by sin c = 1/n.

Example: For glass with n = 1.5, sin c = 1/1.5 = 0.6667, so c = sin⁻¹(0.6667) ≈ 41.8°.

If the angle of incidence is greater than 41.8°, total internal reflection occurs and all light is reflected back into the glass.

• Calculate critical angle using sin c = 1/n.
• Example: n = 1.5 → c ≈ 41.8°.
• If angle of incidence i > c, total internal reflection occurs.

Apparatus: semicircular glass block, laser or ray box, protractor, white paper, pencil, ruler.

Method: Direct a narrow beam of light through the flat face of the semicircular block so it strikes the curved surface at varying angles of incidence.

Measure the angle of incidence and observe the refracted and reflected rays at the curved surface boundary with air. Increase the angle of incidence until the refracted ray disappears and only reflection is seen, indicating total internal reflection occurs beyond the critical angle.

• Independent variable: angle of incidence at curved surface.
• Dependent variable: presence or absence of refracted ray; angle of refraction if present.
• Control variables: wavelength of light, medium (air), block material.
• Repeat measurements to improve accuracy and calculate average critical angle.
• Safety: avoid direct eye exposure to laser beam; handle glass block carefully to prevent breakage and cuts.

Optical fibres use total internal reflection to transmit light signals over long distances with minimal loss. Light entering the fibre is kept inside by repeated total internal reflections at the core-cladding boundary.

Prisms use total internal reflection to reflect light efficiently without loss, for example in binoculars and periscopes.

These applications rely on the principle that light is confined within a medium by total internal reflection, enabling efficient light guidance and redirection.

• Optical fibres: light signals guided by TIR for telecommunications and medical endoscopy.
• Prisms: use TIR to reflect light at precise angles without loss.
• TIR enables efficient light transmission and reflection in various optical devices.

The refractive index, denoted by the symbol n, is a dimensionless quantity that describes how much the speed of a wave, such as light, changes when it passes from one medium into another.

It is defined as the ratio of the speed of the wave in the first medium to the speed of the wave in the second medium.

Mathematically, if v₁ is the speed of light in medium 1 and v₂ is the speed of light in medium 2, then the refractive index n of medium 2 relative to medium 1 is given by: n = v₁ / v₂.

• Refractive index (n) = speed of wave in first medium (v₁) ÷ speed of wave in second medium (v₂)
• Dimensionless quantity (no units)
• Usually, medium 1 is air or vacuum, where light speed is highest

Light travels fastest in a vacuum, at approximately 3.0 × 10⁸ m/s, denoted by c.

When light enters a medium such as glass or water, it slows down due to interactions with the material.

The refractive index quantifies this slowing down: a higher refractive index means the wave travels more slowly in that medium compared to the first medium (usually air or vacuum).

• Speed of light in vacuum, c = 3.0 × 10⁸ m/s
• Speed of light in medium, v < c
• Refractive index n = c / v ≥ 1
• Example: glass has n ≈ 1.5, so light travels at about 2.0 × 10⁸ m/s in glass

The most common form of the refractive index formula uses vacuum as the first medium: n = c / v, where c is the speed of light in vacuum and v is the speed in the medium.

If the speeds in two arbitrary media are known, the refractive index of medium 2 relative to medium 1 is n = v₁ / v₂.

Example calculation: If light travels at 2.0 × 10⁸ m/s in glass, find the refractive index of glass relative to vacuum.

• Given: c = 3.0 × 10⁸ m/s, v = 2.0 × 10⁸ m/s
• Calculate: n = c / v = (3.0 × 10⁸ m/s) / (2.0 × 10⁸ m/s) = 1.5
• Interpretation: Light slows down by a factor of 1.5 in glass compared to vacuum

To visualise refraction, draw a boundary between two media (e.g., air and glass).

Draw the normal line perpendicular to the boundary.

Draw an incident ray approaching the boundary at an angle of incidence i to the normal in the first medium (air). The refracted ray bends towards the normal in the second medium (glass) because light slows down (higher n).

• Normal line: perpendicular to boundary
• Incident ray: angle i to normal in medium 1
• Refracted ray: angle r to normal in medium 2
• Since n₂ > n₁, refracted ray bends towards normal (r < i)

Refractive index is dimensionless; it has no units because it is a ratio of speeds with the same units.

It is incorrect to say refractive index is the ratio of speeds in the order medium 2 over medium 1; the correct order is speed in first medium divided by speed in second medium.

Refractive index always equals or exceeds 1 when the first medium is vacuum or air, because light slows down in other media.

• n = v₁ / v₂, not v₂ / v₁
• No units for refractive index
• n ≥ 1 when first medium is vacuum or air

Refraction is the change in direction of light when it passes from one transparent medium to another, caused by a change in the speed of light in different media.

At the boundary between two media, the angle of incidence (i) is the angle between the incident ray and the normal line, which is an imaginary line perpendicular to the surface at the point of incidence.

The angle of refraction (r) is the angle between the refracted ray and the normal line inside the second medium. Both angles are measured from the normal, not the surface.

• Normal line: perpendicular to the boundary surface at the point of incidence.
• Angle of incidence (i): between incident ray and normal.
• Angle of refraction (r): between refracted ray and normal.

The refractive index (n) of a transparent material is a measure of how much the light slows down and bends when entering that material from air (or another medium).

It is defined by the ratio of the sine of the angle of incidence to the sine of the angle of refraction:

n = sin i / sin r, where i and r are in degrees or radians but the sine function is dimensionless.

• Refractive index is always greater than or equal to 1.
• For air, n ≈ 1 (by definition).
• Higher n means light slows down more and bends more towards the normal.

This formula allows calculation of the refractive index of a material if the angles of incidence and refraction are known.

It can also be rearranged to find unknown angles if n and one angle are known.

Example calculation: Given i = 40° and r = 25°, calculate n: n = sin 40° / sin 25° = 0.6428 / 0.4226 = 1.52 (to 2 decimal places).

• Rearranged forms: sin r = sin i / n, sin i = n × sin r.
• Always use a calculator in degree mode if angles are in degrees.
• Check units and ensure angles are measured from the normal.

To draw a ray diagram showing refraction: first draw a straight horizontal boundary line between two media.

At the point where the ray meets the boundary, draw a normal line perpendicular to the boundary.

Draw the incident ray approaching the boundary at angle i to the normal in the first medium (usually air). Then draw the refracted ray bending towards or away from the normal in the second medium at angle r, according to Snell's law and the refractive indices of the media.

• Label angles i and r clearly from the normal.
• Indicate the two media (e.g., air and glass).
• Show the direction of the ray with arrows.

A common mistake is measuring angles from the surface instead of the normal line; always measure angles from the normal.

Another error is mixing up sine and angle values; use the sine function on the calculator, do not confuse sin i with i.

When calculating refractive index, ensure the angle of incidence is in the medium with refractive index 1 (usually air) and the angle of refraction is in the other medium, or adjust accordingly if the light travels from a denser to a rarer medium.

• Always label angles and normal clearly in diagrams.
• Use consistent units and calculator settings.
• Show all working steps in calculations for full marks.

When light passes from one transparent medium to another, its speed changes, causing the light to change direction; this is called refraction.

The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in that medium: n = c/v, where c is the speed of light in vacuum and v is the speed in the medium.

Refractive index is a dimensionless quantity and is always greater than or equal to 1 for transparent materials.

• Refractive index, n = speed of light in vacuum / speed of light in medium
• Unit of refractive index: none (dimensionless)

When light travels from a denser medium (higher refractive index) to a rarer medium (lower refractive index), the angle of refraction increases as the angle of incidence increases.

At a particular angle of incidence, called the critical angle (c), the angle of refraction is 90°, meaning the refracted ray travels along the boundary between the two media.

If the angle of incidence exceeds the critical angle, no refraction occurs; instead, all the light is reflected back into the denser medium. This phenomenon is called total internal reflection (TIR).

• Critical angle (c): angle of incidence in denser medium for which angle of refraction is 90°
• Total internal reflection occurs when angle of incidence > critical angle
• Condition for TIR: light must travel from denser to rarer medium

Using Snell's law: n₁ sin i = n₂ sin r, where n₁ and n₂ are refractive indices of the first and second media, and i and r are the angles of incidence and refraction respectively.

For critical angle c, the angle of refraction r = 90°, so sin r = sin 90° = 1.

Assuming light travels from a medium with refractive index n (denser) to air with refractive index 1 (rarer), Snell's law becomes: n × sin c = 1 × 1, or n sin c = 1, rearranged as n = 1 / sin c.

• Snell's law: n₁ sin i = n₂ sin r
• At critical angle: r = 90°, so sin r = 1
• Formula: n = 1 / sin c (for light from medium to air)

Calculate the critical angle for light travelling from glass (n = 1.5) to air.

Using the formula n = 1 / sin c, rearranged to find sin c = 1 / n.

Substitute n = 1.5: sin c = 1 / 1.5 = 0.6667 (to 4 decimal places). Using a calculator, c = sin⁻¹(0.6667) ≈ 41.8°.

• Formula: sin c = 1 / n
• Substitution: sin c = 1 / 1.5 = 0.6667
• Calculation: c = sin⁻¹(0.6667) ≈ 41.8°

1. Draw a horizontal boundary line separating two media: the denser medium (e.g., glass) below and the rarer medium (e.g., air) above.

2. Draw the normal line perpendicular to the boundary at the point of incidence.

3. Draw an incident ray in the denser medium approaching the boundary at the critical angle c to the normal, so that the refracted ray lies along the boundary (90° to the normal). Label the angle of incidence as c and the angle of refraction as 90° (ray along the boundary). This illustrates the critical angle condition for refraction.

• Boundary between denser and rarer media
• Normal line perpendicular to boundary
• Incident ray at critical angle c
• Refracted ray along boundary (90° to normal)

An optical fibre is a very thin, flexible strand made of glass or plastic designed to carry light signals over long distances.

It consists of a core surrounded by a cladding layer with a lower refractive index. This difference in refractive indices allows light to be trapped inside the core by total internal reflection.

Light entering the fibre at a suitable angle is reflected repeatedly along the length of the fibre without escaping, enabling efficient transmission.

• Core: central region where light travels, made of glass or plastic with high refractive index.
• Cladding: outer layer with lower refractive index to keep light confined by total internal reflection.
• Total internal reflection occurs when light hits the core-cladding boundary at an angle greater than the critical angle.

Total internal reflection is the key physical principle that allows optical fibres to transmit light signals with minimal loss.

When light travelling in the core strikes the boundary with the cladding at an angle greater than the critical angle, it is completely reflected back into the core rather than refracted out.

This process repeats along the fibre, guiding the light through bends and curves without significant leakage or attenuation.

• Critical angle depends on the refractive indices of core and cladding: sin c = n_cladding / n_core.
• Light must enter the fibre within the acceptance angle to ensure total internal reflection.
• This principle allows signals to travel long distances with low loss.

Optical fibres offer several advantages over traditional copper cables for data transmission:

They provide much higher bandwidth, allowing more data to be transmitted per second.

Signal loss is significantly lower, enabling longer transmission distances without the need for repeaters or amplifiers as frequently as copper cables require.

• Immunity to electromagnetic interference, as light signals are not affected by electrical noise.
• Light signals can carry data at very high speeds, supporting internet, telephone, and television services.
• Optical fibres are thinner and lighter than copper cables, making installation easier and more flexible.

Optical fibres are widely used in telecommunications networks to transmit voice, data, and video signals.

They form the backbone of internet infrastructure, connecting cities and countries with high-speed data links.

Optical fibres are also used in local area networks (LANs), cable television distribution, and telephone systems to improve signal quality and capacity.

• Long-distance communication links between telephone exchanges and internet service providers.
• Undersea fibre optic cables connecting continents.
• High-speed data transmission within buildings and campuses.