Light
Reflection of Light
When light hits a smooth surface (like a mirror), it bounces back. This is called reflection. To describe this accurately, we use specific geometric terms relative to the surface.
The Law of Reflection: The angle of incidence is always equal to the angle of reflection. This applies to all smooth surfaces.
i = r_{refl}
Normal
An imaginary line drawn perpendicular (at 90°) to the reflecting surface at the point where the light ray hits.
Angle of Incidence (i)
The angle between the incident ray (incoming light) and the normal.
Angle of Reflection (r_{refl})
The angle between the reflected ray (outgoing light) and the normal. Note: We use r_{refl} here to distinguish it from the angle of refraction used later.
Plane Mirrors and Image Formation
A plane mirror is a flat, smooth reflecting surface. It forms an image by reflecting light rays from an object into the observer's eye.
Characteristics of an Image in a Plane Mirror:
- Same size as the object.
- Same distance behind the mirror as the object is in front.
- Virtual (cannot be caught on a screen).
- Laterally inverted (left becomes right).
Virtual Image
An image formed where light rays appear to diverge from, but do not actually pass through. Because the light does not physically converge there, a virtual image cannot be projected onto a screen.
Calculations and Constructions for Plane Mirrors (Supplement)
You must be able to construct ray diagrams and calculate image positions. The key principle is that the object distance (d_o) equals the image distance (d_i).
Construction Steps:
- Draw the mirror as a straight line.
- Draw the normal at the point where the light hits.
- Measure angle i and draw the reflected ray such that r_{refl} = i.
- To locate the image: Extend the reflected rays backwards behind the mirror using dashed lines. The point where these dashed lines intersect is the top of the virtual image.
Calculating Image Position
Question: An object is placed 8 cm in front of a plane mirror. Calculate the distance of the image from the mirror.
Solution: For a plane mirror, the image distance equals the object distance.
d_i = d_o
d_i = 8 \text{ cm}
The image is formed 8 cm behind the mirror.
⚠︎ Confusing Real and Virtual Images
Error: Thinking the image in a plane mirror is 'real' because you can see it.
Correction: An image is only 'real' if light rays physically converge at that point (like on a cinema screen). In a plane mirror, your eye traces diverging rays back to a point where no light exists. Therefore, the image is virtual.
Correction: An image is only 'real' if light rays physically converge at that point (like on a cinema screen). In a plane mirror, your eye traces diverging rays back to a point where no light exists. Therefore, the image is virtual.
Describing Plane Mirror Images
When to use: When asked to describe the image formed by a plane mirror.
Why examiners accept this: Examiners look for specific keywords that define the nature of the image. 'Virtual' is crucial because it distinguishes it from real images formed by lenses or curved mirrors.
Correct phrasing: "The image is virtual, upright, same size as the object, and laterally inverted."
Example: If asked why you cannot project a clock's reflection onto a wall behind the mirror, answer: "Because the image is virtual; light rays do not actually pass through the image position."
Why examiners accept this: Examiners look for specific keywords that define the nature of the image. 'Virtual' is crucial because it distinguishes it from real images formed by lenses or curved mirrors.
Correct phrasing: "The image is virtual, upright, same size as the object, and laterally inverted."
Example: If asked why you cannot project a clock's reflection onto a wall behind the mirror, answer: "Because the image is virtual; light rays do not actually pass through the image position."
Reflection and Plane Mirrors
Q:
State the law of reflection.
A:
The angle of incidence is equal to the angle of reflection.
Q:
Describe two characteristics of an image formed by a plane mirror.
A:
- The image is virtual.
- The image is the same size as the object (or same distance behind the mirror).
Refraction of Light
Refraction is the change in direction of a light wave as it passes from one transparent medium to another (e.g., air to glass). This happens because light changes speed.
Key Terms:
- Normal: The line perpendicular to the boundary between the two media.
- Angle of Incidence (i): Angle between incident ray and normal.
- Angle of Refraction (r_{refr}): Angle between refracted ray and normal.
Note on Notation: In this section, r (or r_{refr}) refers to the Angle of Refraction. Do not confuse it with the Angle of Reflection (r_{refl}) used in the previous section.
Rules of Refraction:
- Air to Glass/Water (Less dense to More dense): Light slows down and bends towards the normal (i > r_{refr}).
- Glass/Water to Air (More dense to Less dense): Light speeds up and bends away from the normal (i < r_{refr}).
Experiment: Refraction through Transparent Blocks
Aim: To investigate the relationship between angle of incidence and angle of refraction.
Apparatus: Ray box, rectangular glass block, protractor, paper, pencil.
Method:
- Place the glass block on paper and trace its outline.
- Draw a normal line perpendicular to one side of the block.
- Shine a ray of light at an angle (e.g., 30°) along the normal. Mark the incident ray with two dots.
- Observe the emergent ray on the other side. Place two pins (P3, P4) so they align with the images of the first two pins (P1, P2).
- Remove the block and draw a straight line through P3 and P4 to complete the refracted and emergent rays.
- Measure the angle of refraction (r_{refr}) inside the block.
- Repeat for different angles of incidence.
Critical Angle and Total Internal Reflection (TIR)
Total Internal Reflection (TIR) occurs when:
- Light travels from a denser medium to a less dense medium.
- The angle of incidence is greater than the critical angle (i > c).
When TIR occurs, no light is refracted. All light is reflected back into the denser medium, obeying the law of reflection (i = r_{refl}).
Everyday Examples:
- Prisms in binoculars: Use TIR to reflect light 90° or 180°, providing brighter images than mirrors.
- Optical Fibres: Light travels down the fibre by undergoing continuous TIR along the core-cladding boundary.
Critical Angle (c)
The angle of incidence in the denser medium (e.g., glass) for which the angle of refraction in the less dense medium (e.g., air) is exactly 90°.
Refractive Index (n)
Snell's Law (Calculation):
n = \frac{\sin i}{\sin r_{refr}}
Where i is the angle in air/vacuum and r_{refr} is the angle in the medium.
n = \frac{\sin i}{\sin r_{refr}}
Where i is the angle in air/vacuum and r_{refr} is the angle in the medium.
Critical Angle Formula:
n = \frac{1}{\sin c}
Derived from Snell's Law by setting r_{refr} = 90° (so \sin 90° = 1).
Refractive Index
A measure of how much light slows down in a material compared to vacuum (or air). It is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v).
n = \frac{c}{v}
Since c > v, n is always greater than 1.
Calculating Refractive Index and Critical Angle
Question 1: Light enters glass from air. i = 30°, r_{refr} = 19°. Calculate n.
n = \frac{\sin 30°}{\sin 19°} = \frac{0.500}{0.326} \approx 1.53
n = \frac{\sin 30°}{\sin 19°} = \frac{0.500}{0.326} \approx 1.53
Question 2: If the refractive index of a material is 1.5, calculate its critical angle.
n = \frac{1}{\sin c} \Rightarrow 1.5 = \frac{1}{\sin c}
\sin c = \frac{1}{1.5} = 0.667
c = \sin^{-1}(0.667) \approx 41.8°
⚠︎ Conditions for Total Internal Reflection
Error: Believing TIR can occur when light travels from air into glass.
Correction: TIR only occurs when light travels from a denser medium (slower speed) to a less dense medium (faster speed). If light goes air-to-glass, it always refracts away from the normal; it never reflects internally.
Correction: TIR only occurs when light travels from a denser medium (slower speed) to a less dense medium (faster speed). If light goes air-to-glass, it always refracts away from the normal; it never reflects internally.
Describing Optical Fibres
When to use: When asked to explain how optical fibres work or their advantage in telecommunications.
Why examiners accept this: You must link the physical phenomenon (TIR) to the function (signal transmission).
Correct phrasing: "Light signals undergo total internal reflection at the boundary between the core and cladding because the angle of incidence is greater than the critical angle. This allows light to travel long distances with minimal loss of energy (or signal attenuation)."
Example: "Explain why optical fibres are better than copper wires." Answer: "Optical fibres use TIR, so there is no electrical resistance and less signal degradation over distance."
Why examiners accept this: You must link the physical phenomenon (TIR) to the function (signal transmission).
Correct phrasing: "Light signals undergo total internal reflection at the boundary between the core and cladding because the angle of incidence is greater than the critical angle. This allows light to travel long distances with minimal loss of energy (or signal attenuation)."
Example: "Explain why optical fibres are better than copper wires." Answer: "Optical fibres use TIR, so there is no electrical resistance and less signal degradation over distance."
Refraction and Critical Angle
Q:
Define the critical angle.
A:
The angle of incidence in the denser medium for which the angle of refraction is 90°.
Q:
State two conditions necessary for total internal reflection to occur.
A:
- Light must travel from a denser medium to a less dense medium.
- The angle of incidence must be greater than the critical angle.
Q:
Calculate the refractive index if the critical angle is 42°.
A:
$ n = 1 / \sin(42°) = 1.49 $
Converging Lens (Convex)
A lens that is thicker in the middle than at the edges. It causes parallel rays of light to converge (meet) at a point.
Diverging Lens (Concave)
A lens that is thinner in the middle than at the edges. It causes parallel rays of light to diverge (spread out).
Principal Axis
The line passing through the center of the lens, perpendicular to its surface.
Principal Focus (Focal Point)
The point on the principal axis where parallel rays converge (for converging lens) or appear to diverge from (for diverging lens).
Focal Length (f)
The distance from the center of the lens to the principal focus.
Ray Diagrams for Converging Lenses
To draw a ray diagram, use two of the following three principal rays:
- Parallel Ray: A ray parallel to the principal axis refracts through the principal focus (F) on the other side.
- Central Ray: A ray passing through the center of the lens continues undeviated (in a straight line).
- Focal Ray: A ray passing through the principal focus (F) before hitting the lens refracts parallel to the principal axis.
Real Image Formation:
- Occurs when the object is outside the focal point (u > f).
- The rays actually converge at a point.
- The image is inverted and can be projected on a screen.
Virtual Image by Converging Lens (Supplement)
Formation: Occurs when the object is inside the focal point (u < f). This is how a magnifying glass works.
Construction Steps:
- Draw the parallel ray from the top of the object: it refracts through F on the far side.
- Draw the central ray from the top of the object: it goes straight through the center.
- The two refracted rays are now diverging (moving apart). They will never meet on the right side.
- Extend the refracted parallel ray backwards (using a dashed line) behind the lens.
- Where this dashed line meets the central ray is the top of the virtual image.
Virtual Image Characteristics
For a converging lens used as a magnifier:
- Upright (same orientation as object)
- Enlarged (magnified)
- Virtual (formed on the same side as the object)
Describing Image Characteristics
Question: Describe the image formed by a converging lens when the object is placed at a distance greater than twice the focal length (u > 2f).
Answer: The image is real, inverted, and diminished (smaller than the object).
⚠︎ Vision Defects Correction
Error: Thinking short-sightedness (myopia) is corrected with a converging lens.
Correction:
- Short-sightedness: Image forms in front of the retina. Needs a diverging lens to spread light out before it enters the eye.
- Long-sightedness: Image forms behind the retina. Needs a converging lens to bend light inwards earlier.
Correcting Vision Defects
When to use: When asked how a lens corrects long-sightedness or short-sightedness.
Why examiners accept this: You must explain the effect of the lens on the light path relative to the retina.
Correct phrasing for Long-sightedness: "A converging lens is used. It converges the incoming light rays so that they focus on the retina instead of behind it."
Example: "Explain why a long-sighted person needs a convex lens." Answer: "The eye's lens is too weak, so images form behind the retina. A convex (converging) lens adds convergence, moving the focal point forward onto the retina."
Why examiners accept this: You must explain the effect of the lens on the light path relative to the retina.
Correct phrasing for Long-sightedness: "A converging lens is used. It converges the incoming light rays so that they focus on the retina instead of behind it."
Example: "Explain why a long-sighted person needs a convex lens." Answer: "The eye's lens is too weak, so images form behind the retina. A convex (converging) lens adds convergence, moving the focal point forward onto the retina."
Lenses and Vision
Q:
Describe how a converging lens corrects long-sightedness.
A:
It converges light rays so that they focus on the retina instead of behind it.
Q:
State two characteristics of an image formed by a magnifying glass (converging lens with object inside F).
A:
- Virtual
- Upright (or Enlarged)
Dispersion of Light
Dispersion is the splitting of white light into its constituent colours when it passes through a prism.
Why it happens: Different colours (frequencies) of light travel at slightly different speeds in glass, so they refract by different amounts. Violet bends the most; Red bends the least.
Visible Spectrum Colours
The seven colours in order of increasing frequency (and decreasing wavelength):
- Red
- Orange
- Yellow
- Green
- Blue
- Indigo
- Violet
Mnemonic: Red Orange Yellow Green Blue Indigo Violet (ROYGBIV).
Monochromatic Light
Light of a single frequency (and therefore single colour/wavelength). Example: Laser light.
Dispersion and Spectrum
Q:
Name the process that splits white light into colours.
A:
Dispersion.
Q:
Which colour of light is refracted the most by a glass prism?
A:
Violet.
Q:
What is monochromatic light?
A:
Light of a single frequency (or single wavelength).
Reflection and Plane Mirrors
Q:
State the law of reflection.
A:
The angle of incidence is equal to the angle of reflection.
Q:
Describe two characteristics of an image formed by a plane mirror.
A:
- The image is virtual.
- The image is the same size as the object (or same distance behind the mirror).
Refraction of Light
Refraction is the change in direction of a light wave as it passes from one transparent medium to another (e.g., air to glass). This happens because light changes speed.
Key Terms:
- Normal: The line perpendicular to the boundary between the two media.
- Angle of Incidence (i): Angle between incident ray and normal.
- Angle of Refraction (r_{refr}): Angle between refracted ray and normal.
Note on Notation: In this section, r (or r_{refr}) refers to the Angle of Refraction. Do not confuse it with the Angle of Reflection (r_{refl}) used in the previous section.
Rules of Refraction:
- Air to Glass/Water (Less dense to More dense): Light slows down and bends towards the normal (i > r_{refr}).
- Glass/Water to Air (More dense to Less dense): Light speeds up and bends away from the normal (i < r_{refr}).
Experiment: Refraction through Transparent Blocks
Aim: To investigate the relationship between angle of incidence and angle of refraction.
Apparatus: Ray box, rectangular glass block, protractor, paper, pencil.
Method:
- Place the glass block on paper and trace its outline.
- Draw a normal line perpendicular to one side of the block.
- Shine a ray of light at an angle (e.g., 30°) along the normal. Mark the incident ray with two dots.
- Observe the emergent ray on the other side. Place two pins (P3, P4) so they align with the images of the first two pins (P1, P2).
- Remove the block and draw a straight line through P3 and P4 to complete the refracted and emergent rays.
- Measure the angle of refraction (r_{refr}) inside the block.
- Repeat for different angles of incidence.
Critical Angle and Total Internal Reflection (TIR)
Total Internal Reflection (TIR) occurs when:
- Light travels from a denser medium to a less dense medium.
- The angle of incidence is greater than the critical angle (i > c).
When TIR occurs, no light is refracted. All light is reflected back into the denser medium, obeying the law of reflection (i = r_{refl}).
Everyday Examples:
- Prisms in binoculars: Use TIR to reflect light 90° or 180°, providing brighter images than mirrors.
- Optical Fibres: Light travels down the fibre by undergoing continuous TIR along the core-cladding boundary.
Critical Angle (c)
The angle of incidence in the denser medium (e.g., glass) for which the angle of refraction in the less dense medium (e.g., air) is exactly 90°.
Refractive Index (n)
Snell's Law (Calculation):
n = \frac{\sin i}{\sin r_{refr}}
Where i is the angle in air/vacuum and r_{refr} is the angle in the medium.
n = \frac{\sin i}{\sin r_{refr}}
Where i is the angle in air/vacuum and r_{refr} is the angle in the medium.
Critical Angle Formula:
n = \frac{1}{\sin c}
Derived from Snell's Law by setting r_{refr} = 90° (so \sin 90° = 1).
Refractive Index
A measure of how much light slows down in a material compared to vacuum (or air). It is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v).
n = \frac{c}{v}
Since c > v, n is always greater than 1.
Calculating Refractive Index and Critical Angle
Question 1: Light enters glass from air. i = 30°, r_{refr} = 19°. Calculate n.
n = \frac{\sin 30°}{\sin 19°} = \frac{0.500}{0.326} \approx 1.53
n = \frac{\sin 30°}{\sin 19°} = \frac{0.500}{0.326} \approx 1.53
Question 2: If the refractive index of a material is 1.5, calculate its critical angle.
n = \frac{1}{\sin c} \Rightarrow 1.5 = \frac{1}{\sin c}
\sin c = \frac{1}{1.5} = 0.667
c = \sin^{-1}(0.667) \approx 41.8°
⚠︎ Conditions for Total Internal Reflection
Error: Believing TIR can occur when light travels from air into glass.
Correction: TIR only occurs when light travels from a denser medium (slower speed) to a less dense medium (faster speed). If light goes air-to-glass, it always refracts away from the normal; it never reflects internally.
Correction: TIR only occurs when light travels from a denser medium (slower speed) to a less dense medium (faster speed). If light goes air-to-glass, it always refracts away from the normal; it never reflects internally.
Describing Optical Fibres
When to use: When asked to explain how optical fibres work or their advantage in telecommunications.
Why examiners accept this: You must link the physical phenomenon (TIR) to the function (signal transmission).
Correct phrasing: "Light signals undergo total internal reflection at the boundary between the core and cladding because the angle of incidence is greater than the critical angle. This allows light to travel long distances with minimal loss of energy (or signal attenuation)."
Example: "Explain why optical fibres are better than copper wires." Answer: "Optical fibres use TIR, so there is no electrical resistance and less signal degradation over distance."
Why examiners accept this: You must link the physical phenomenon (TIR) to the function (signal transmission).
Correct phrasing: "Light signals undergo total internal reflection at the boundary between the core and cladding because the angle of incidence is greater than the critical angle. This allows light to travel long distances with minimal loss of energy (or signal attenuation)."
Example: "Explain why optical fibres are better than copper wires." Answer: "Optical fibres use TIR, so there is no electrical resistance and less signal degradation over distance."
Refraction and Critical Angle
Q:
Define the critical angle.
A:
The angle of incidence in the denser medium for which the angle of refraction is 90°.
Q:
State two conditions necessary for total internal reflection to occur.
A:
- Light must travel from a denser medium to a less dense medium.
- The angle of incidence must be greater than the critical angle.
Q:
Calculate the refractive index if the critical angle is 42°.
A:
$ n = 1 / \sin(42°) = 1.49 $
Converging Lens (Convex)
A lens that is thicker in the middle than at the edges. It causes parallel rays of light to converge (meet) at a point.
Diverging Lens (Concave)
A lens that is thinner in the middle than at the edges. It causes parallel rays of light to diverge (spread out).
Principal Axis
The line passing through the center of the lens, perpendicular to its surface.
Principal Focus (Focal Point)
The point on the principal axis where parallel rays converge (for converging lens) or appear to diverge from (for diverging lens).
Focal Length (f)
The distance from the center of the lens to the principal focus.
Ray Diagrams for Converging Lenses
To draw a ray diagram, use two of the following three principal rays:
- Parallel Ray: A ray parallel to the principal axis refracts through the principal focus (F) on the other side.
- Central Ray: A ray passing through the center of the lens continues undeviated (in a straight line).
- Focal Ray: A ray passing through the principal focus (F) before hitting the lens refracts parallel to the principal axis.
Real Image Formation:
- Occurs when the object is outside the focal point (u > f).
- The rays actually converge at a point.
- The image is inverted and can be projected on a screen.
Virtual Image by Converging Lens (Supplement)
Formation: Occurs when the object is inside the focal point (u < f). This is how a magnifying glass works.
Construction Steps:
- Draw the parallel ray from the top of the object: it refracts through F on the far side.
- Draw the central ray from the top of the object: it goes straight through the center.
- The two refracted rays are now diverging (moving apart). They will never meet on the right side.
- Extend the refracted parallel ray backwards (using a dashed line) behind the lens.
- Where this dashed line meets the central ray is the top of the virtual image.
Virtual Image Characteristics
For a converging lens used as a magnifier:
- Upright (same orientation as object)
- Enlarged (magnified)
- Virtual (formed on the same side as the object)
Describing Image Characteristics
Question: Describe the image formed by a converging lens when the object is placed at a distance greater than twice the focal length (u > 2f).
Answer: The image is real, inverted, and diminished (smaller than the object).
⚠︎ Vision Defects Correction
Error: Thinking short-sightedness (myopia) is corrected with a converging lens.
Correction:
- Short-sightedness: Image forms in front of the retina. Needs a diverging lens to spread light out before it enters the eye.
- Long-sightedness: Image forms behind the retina. Needs a converging lens to bend light inwards earlier.
Correcting Vision Defects
When to use: When asked how a lens corrects long-sightedness or short-sightedness.
Why examiners accept this: You must explain the effect of the lens on the light path relative to the retina.
Correct phrasing for Long-sightedness: "A converging lens is used. It converges the incoming light rays so that they focus on the retina instead of behind it."
Example: "Explain why a long-sighted person needs a convex lens." Answer: "The eye's lens is too weak, so images form behind the retina. A convex (converging) lens adds convergence, moving the focal point forward onto the retina."
Why examiners accept this: You must explain the effect of the lens on the light path relative to the retina.
Correct phrasing for Long-sightedness: "A converging lens is used. It converges the incoming light rays so that they focus on the retina instead of behind it."
Example: "Explain why a long-sighted person needs a convex lens." Answer: "The eye's lens is too weak, so images form behind the retina. A convex (converging) lens adds convergence, moving the focal point forward onto the retina."
Lenses and Vision
Q:
Describe how a converging lens corrects long-sightedness.
A:
It converges light rays so that they focus on the retina instead of behind it.
Q:
State two characteristics of an image formed by a magnifying glass (converging lens with object inside F).
A:
- Virtual
- Upright (or Enlarged)
Dispersion of Light
Dispersion is the splitting of white light into its constituent colours when it passes through a prism.
Why it happens: Different colours (frequencies) of light travel at slightly different speeds in glass, so they refract by different amounts. Violet bends the most; Red bends the least.
Visible Spectrum Colours
The seven colours in order of increasing frequency (and decreasing wavelength):
- Red
- Orange
- Yellow
- Green
- Blue
- Indigo
- Violet
Mnemonic: Red Orange Yellow Green Blue Indigo Violet (ROYGBIV).
Monochromatic Light
Light of a single frequency (and therefore single colour/wavelength). Example: Laser light.
Dispersion and Spectrum
Q:
Name the process that splits white light into colours.
A:
Dispersion.
Q:
Which colour of light is refracted the most by a glass prism?
A:
Violet.
Q:
What is monochromatic light?
A:
Light of a single frequency (or single wavelength).