LEARNING OBJECTIVES
What you will be able to do
- construct accurate reflection and refraction ray diagrams
- use refractive index and critical angle equations
- describe images formed by thin converging lenses
- explain dispersion and total internal reflection
AT A GLANCE
INTRODUCTION · THE BIG IDEA
Use ray models to explain reflection, refraction, lenses and optical communication.
Ray diagrams represent the direction in which light energy travels. Careful normals, arrowheads and scaled construction turn an optical situation into a solvable geometry problem.
Refraction, lenses and total internal reflection all follow from changes in wave speed at boundaries.
SECTION 01
Reflection and plane-mirror images
The angle of incidence equals the angle of reflection. A plane mirror forms an image that is virtual, upright, laterally inverted, the same size as the object and the same distance behind the mirror as the object is in front.
A virtual image occurs where rays appear to meet and cannot be projected onto a screen. Extend reflected rays backward with dashed lines to locate it.
SECTION 02
Refraction and refractive index
Light bends toward the normal when it slows on entering a more optically dense medium, and away when it speeds up. The refractive index compares light speed in vacuum with speed in the material.
For a rectangular block, the emergent ray is parallel to the incident ray but laterally displaced. Apparent depth occurs because rays leaving water bend away from the normal.
Calculating refractive index
- Light enters glass with i = 50° and r = 30°.
- n = sin 50° ÷ sin 30°.
- Use angles measured from the normal.
Answer: n = 1.53 to 3 significant figures.
SECTION 03
Thin converging lenses
A ray parallel to the principal axis refracts through the far focus; a ray through the optical centre continues undeviated. Their intersection locates a real image.
An object beyond 2F gives a smaller real image; at 2F, equal size; between F and 2F, enlarged real image; inside F, an enlarged upright virtual image. A magnifying glass uses the final case.
Image magnification
- An object is 12 mm high.
- Its real image is 36 mm high.
- Magnification = 36 ÷ 12.
Answer: Magnification = 3.0.
SECTION 04
Total internal reflection and dispersion
Total internal reflection occurs only when light travels from higher to lower refractive index and the incidence angle exceeds the critical angle. Optical fibres guide light by repeated internal reflection and are used in communication and endoscopes.
White light disperses because refractive index depends on wavelength. Violet light changes speed and direction more than red light in glass, spreading the spectrum.
Critical angle of glass
- Glass has refractive index 1.50.
- sin c = 1/1.50 = 0.667.
- c = sin⁻¹(0.667).
Answer: Critical angle ≈ 41.8°.
QUICK CHAPTER SUMMARY
The ideas to carry forward
- Measure every optical angle from the normal.
- Refraction results from a change in wave speed.
- Two principal rays are enough to locate a lens image.
- Total internal reflection needs the correct direction and an angle above the critical angle.
QUICK REVISION CHECKLIST
Can you do each of these without your notes?
- construct accurate reflection and refraction ray diagrams
- use refractive index and critical angle equations
- describe images formed by thin converging lenses
- explain dispersion and total internal reflection