Chapter: Light
Welcome to your study guide on Light! Light is all around us—it lets you read these words, enjoy the colours of a sunset, and communicate across the globe through ultra-fast fibre broadband. In this chapter, we will explore how light travels, bounces (reflection), bends (refraction), gets trapped (total internal reflection), focuses through lenses, and splits into a rainbow of colours (dispersion).
Don't worry if physics sometimes feels tricky! We will break everything down into bite-sized steps with clear rules, everyday analogies, and helpful memory tricks.
---1. How Light Travels and the Law of Reflection
The Basics of Light
Light is a transverse wave that transfers energy. Unlike sound waves, light does not need particles to travel, which means it can travel through a vacuum (empty space).
• Speed of light in a vacuum/air: \(c = 3 \times 10^8\text{ m/s}\) (that is \(300,000,000\text{ metres per second}\)—the fastest speed in the universe!)
• Light always travels in straight lines in a uniform medium. We represent light using straight lines with arrows called rays.
Reflection at a Plane (Flat) Mirror
When a ray of light hits a smooth surface like a plane mirror, it bounces off. To describe this mathematically, we draw a reference line called the normal.
Key Terminology:
• Normal: An imaginary dashed line drawn at a right angle (\(90^\circ\)) to the reflective surface at the point where the light ray hits.
• Incident Ray: The ray of light travelling towards the mirror.
• Reflected Ray: The ray of light bouncing away from the mirror.
• Angle of Incidence (\(i\)): The angle between the incident ray and the normal.
• Angle of Reflection (\(r\)): The angle between the reflected ray and the normal.
The Law of Reflection
For all reflecting surfaces:
Angle of incidence = Angle of reflection
\(i = r\)
Common Mistake to Avoid: Always measure angles from the normal line, NOT from the mirror's surface!
Properties of an Image in a Plane Mirror
When you look at yourself in a flat bathroom mirror, your reflection has five specific properties:
1. Virtual: The light rays only appear to come from behind the mirror; they do not actually pass through it (it cannot be projected onto a screen).
2. Upright: It is the right way up (not upside down).
3. Same size: The image is identical in height and width to the object.
4. Same distance: The image appears as far behind the mirror as the object is in front of it.
5. Laterally inverted: It is flipped left-to-right (if you raise your right hand, your mirror image raises its left hand).
Key Takeaway: Light travels in straight lines at \(3 \times 10^8\text{ m/s}\). For reflection, the angle of incidence always equals the angle of reflection (\(i = r\)), measured from the normal.
---2. Refraction of Light
What is Refraction?
Refraction is the bending of light when it passes from one transparent material (medium) into another with a different optical density. This bending happens because light changes speed when entering a new material.
• In optically denser materials (like glass, water, or perspex), light travels slower.
• In less dense materials (like air or vacuum), light travels faster.
The Muddy Car Analogy
Imagine a toy car rolling at an angle from a smooth wooden floor onto thick mud:
• The tyre that hits the mud first slows down before the other tyre.
• This causes the car to swivel and bend towards the line perpendicular to the mud border.
• When leaving the mud back onto the wooden floor, the first tyre speeds up, bending the car away.
Rules for Refraction
• From Less Dense to Denser (e.g., Air \(\rightarrow\) Glass): Light slows down and bends TOWARDS the normal (\(i > r\)).
• From Denser to Less Dense (e.g., Glass \(\rightarrow\) Air): Light speeds up and bends AWAY from the normal (\(i < r\)).
• Along the Normal (\(i = 0^\circ\)): If the ray hits the boundary straight on at \(90^\circ\) to the surface, it changes speed but does not bend (\(r = 0^\circ\)).
Memory Aid: FAST
• Faster \(\rightarrow\) Away from normal
• Slower \(\rightarrow\) Towards normal
Passing Through a Rectangular Glass Block
1. As light enters the block (air to glass), it bends towards the normal.
2. As it travels through the parallel sides and exits (glass to air), it bends away from the normal by the exact same amount.
3. Result: The ray coming out (emergent ray) is parallel to the ray going in (incident ray), but shifted slightly sideways.
Key Takeaway: Refraction is caused by a change in wave speed. Slower means bending towards the normal; faster means bending away from the normal.
---3. Total Internal Reflection (TIR)
What Happens as the Angle of Incidence Increases?
When light travels from an optically denser medium (like glass or water) towards a less dense medium (like air):
1. Small angle of incidence (\(i < c\)): Most of the light refracts into the air, bending away from the normal. A tiny amount reflects internally.
2. Critical angle (\(i = c\)): The angle of refraction becomes exactly \(90^\circ\). The refracted light ray travels right along the surface boundary.
3. Angle larger than critical angle (\(i > c\)): No light escapes into the air! 100% of the light reflects back inside the denser medium. This is called Total Internal Reflection (TIR).
Definition: Critical Angle (\(c\))
The critical angle is the angle of incidence in the denser medium for which the angle of refraction is \(90^\circ\).
Did you know? For standard glass, the critical angle is roughly \(42^\circ\). For water, it is approximately \(49^\circ\).
Two Strict Conditions Required for TIR
Total Internal Reflection only occurs if both of these conditions are met:
1. Light must be travelling from an optically denser medium towards a less dense medium (e.g., glass to air).
2. The angle of incidence must be greater than the critical angle (\(i > c\)).
Everyday Applications of TIR
• Optical Fibres: Very thin, flexible strands of high-purity glass. Light signals enter at an angle greater than the critical angle and continuously undergo TIR along the length of the cable. Used in high-speed broadband and medical endoscopes to see inside the human body without invasive surgery.
• Prisms in Periscopes & Binoculars: Right-angled glass prisms bend light by \(90^\circ\) or \(180^\circ\) using TIR. Unlike traditional silvered mirrors, prisms do not produce faint double images and reflect almost \(100\%\) of the light.
• Bicycle Reflectors & Road Studs: Shaped prisms bounce car headlight beams straight back to the driver.
Key Takeaway: When light goes from dense to less dense at an angle greater than the critical angle (\(i > c\)), it is entirely reflected inside the material. This is TIR.
---4. Lenses and Ray Diagrams
Types of Lenses
Lenses work by refracting light at both curved surfaces to bring rays together or spread them apart.
1. Convex (Converging) Lens: Thicker in the middle than at the edges. It brings parallel rays of light together to meet at a single focal point.
2. Concave (Diverging) Lens: Thinner in the middle than at the edges. It causes parallel rays of light to spread out away from a focal point.
Important Lens Terms
• Principal Axis: The straight horizontal line passing right through the optical centre of the lens.
• Principal Focus (\(F\)) / Focal Point: For a convex lens, the point on the principal axis where rays parallel to the axis converge after passing through the lens.
• Focal Length (\(f\)): The distance from the centre of the lens to the principal focus (\(F\)). A fatter/more curved lens has a shorter focal length and higher optical power.
Drawing Ray Diagrams for a Convex Lens
To locate where an image forms, we draw at least two standard rays from the top of the object:
1. Ray 1: Travels parallel to the principal axis, then refracts straight through the principal focus (\(F\)) on the other side.
2. Ray 2: Passes straight through the optical centre of the lens without bending at all.
• The point where these two rays cross is where the top of the image forms.
Describing Images (The 3 Descriptors)
Whenever you describe an image formed by a lens, state all three properties:
• Real or Virtual: A real image can be projected onto a screen (rays actually cross). A virtual image cannot be formed on a screen (rays appear to diverge from a point).
• Inverted or Upright: Inverted means upside down; upright means right side up.
• Magnified, Diminished, or Same Size: Magnified means larger than the object; diminished means smaller than the object.
Image Formation by Convex Lenses:
• Object placed far beyond \(2F\): Real, inverted, diminished (e.g., in a camera or human eye).
• Object placed between \(F\) and \(2F\): Real, inverted, magnified (e.g., in a projector).
• Object placed closer than \(F\): Virtual, upright, magnified (e.g., used as a magnifying glass).
Magnification Formula
Magnification tells you how many times larger or smaller the image is compared to the object:
\(\text{Magnification} = \frac{\text{Image Height}}{\text{Object Height}}\) or \(\text{Magnification} = \frac{\text{Image Distance}}{\text{Object Distance}}\)
Note: Magnification is a ratio and has no units (e.g., \(\times 2\) or \(1.5\)).
Correcting Vision Defects
• Short-sightedness (Myopia): Person can see close objects clearly, but distant objects are blurry because the eye focuses light in front of the retina. Corrected with a diverging (concave) lens.
• Long-sightedness (Hyperopia): Person can see distant objects clearly, but close objects are blurry because the eye focuses light behind the retina. Corrected with a converging (convex) lens.
Key Takeaway: Convex lenses converge light and can make real or virtual images. Concave lenses diverge light and always make virtual, upright, diminished images.
---5. Dispersion and the Visible Spectrum
White Light and the Visible Spectrum
White light from the Sun or a lamp is not a single colour—it is a mixture of all the colours of the visible spectrum.
The colours in order of increasing frequency (and decreasing wavelength) are:
Red, Orange, Yellow, Green, Blue, Indigo, Violet
Memory Trick: Richard Of York Gave Battle In Vain (ROYGBIV).
Dispersion Through a Triangular Prism
When white light enters a triangular glass prism, it splits into its component colours. This separation is called dispersion.
Why Does Dispersion Happen?
• Each colour of light has a different wavelength.
• Red light has the longest wavelength and slows down the least in glass \(\rightarrow\) it is refracted (bent) the least.
• Violet light has the shortest wavelength and slows down the most in glass \(\rightarrow\) it is refracted (bent) the most.
• Because each colour refracts by a slightly different angle at both faces of the prism, the colours spread out into a continuous spectrum.
Key Takeaway: Dispersion splits white light because different colours have different wavelengths and refract by different amounts: Red bends least, Violet bends most.
---Quick Chapter Summary & Exam Checklist
Before sitting your exam, make sure you can:
• State the law of reflection: \(i = r\), with angles measured from the normal.
• State the 5 features of a plane mirror image (virtual, upright, same size, same distance, laterally inverted).
• Explain refraction in terms of speed changes (FAST: Faster = Away, Slower = Towards).
• State the two conditions for Total Internal Reflection (\(i > c\) and dense \(\rightarrow\) less dense).
• Explain how optical fibres work and list applications (telecoms, endoscopes).
• Draw ray diagrams for convex lenses and calculate magnification (\(\text{Magnification} = \frac{\text{Image Height}}{\text{Object Height}}\)).
• State which lenses correct short-sightedness (concave) and long-sightedness (convex).
• Explain dispersion: Red has the longest wavelength (bends least); Violet has the shortest wavelength (bends most).