Light
Section: Waves | Syllabus: Cambridge IGCSE Physics (0625)
Light is a transverse electromagnetic wave that travels at 3 × 10^8 m/s in a vacuum, and obeys the same reflection, refraction and diffraction rules as other waves.
Reflection of Light
- Normal: a line drawn at right angles to a surface, at the point where a ray meets it
- 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
- Law of reflection: the angle of incidence equals the angle of reflection (i = r)
Plane Mirror Images
A plane (flat) mirror forms an image with the following characteristics:
- Same size as the object
- Same distance behind the mirror as the object is in front of it
- Virtual - cannot be projected onto a screen
- Laterally inverted - left and right are swapped
- Upright - the same way up as the object
Formation of an image by a plane mirror
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Constructing Mirror Images
- Mark the image at the same perpendicular distance behind the mirror as the object is in front of it
- To find a reflected ray's path, draw the incident ray to the mirror, construct the reflected ray so that i = r, and, if needed, extend reflected rays backward (as dashed lines) behind the mirror - the point where two extended rays cross locates the image
Worked Example: Locating a Mirror Image
Museli places an object 8 cm in front of a plane mirror. How far behind the mirror does the image form, and what are its characteristics?
- Image distance behind mirror = object distance in front of mirror = 8 cm
- The image is virtual, upright, the same size as the object, and laterally inverted
Refraction of Light
- Normal: a line drawn at right angles to the boundary between two media, at the point where a ray crosses it
- Angle of incidence (i): the angle between the incident ray and the normal, in the first medium
- Angle of refraction (r): the angle between the refracted ray and the normal, in the second medium
- Light bends toward the normal when it slows down entering an optically denser medium, and away from the normal when it speeds up leaving it; its frequency never changes
Investigating Refraction Using Glass Blocks
- Method: place a transparent block (e.g. rectangular, semicircular or triangular) on a sheet of paper and trace its outline; direct a ray of light from a ray box into the block at a measured angle of incidence; mark the ray's path entering and leaving the block, then remove the block and join the marked points with straight lines to show the complete path
- Measure the angle of incidence and angle of refraction at each boundary using a protractor, with both angles measured from the normal
- Repeating with different angles of incidence, and with differently shaped blocks, shows that the ray always bends toward the normal on entering the (optically denser) block, and away from the normal on leaving it
Investigating refraction with a glass block
Passage of Light Through a Transparent Block
- At the first boundary (air to glass), the ray bends toward the normal as it slows down entering the glass
- At the second boundary (glass to air), the ray bends away from the normal as it speeds up leaving the glass
- For a rectangular block, the emergent ray is parallel to the original incident ray, but laterally displaced (shifted sideways) from it
Passage of light through a rectangular glass block
Critical Angle and Total Internal Reflection
- Critical angle (C): the angle of incidence, in the optically denser medium, for which the angle of refraction is 90° - the refracted ray travels along the boundary itself
Internal Reflection and Total Internal Reflection
- Whenever light travelling in an optically denser medium meets a boundary with a less dense medium, some of the light is reflected back into the denser medium - this partial reflection is called internal reflection, and happens at any angle of incidence
- If the angle of incidence is greater than the critical angle (i > C), all of the light is reflected back into the denser medium and none is refracted out - this is total internal reflection (TIR)
Refraction, the critical angle, and total internal reflection
Experimental Example
- Directing a ray of light into the curved side of a semicircular glass block, aimed at the centre of the flat side, allows the angle of incidence at the flat (glass-to-air) surface to be varied without the ray bending on entry
- As the angle of incidence is increased, a faint reflected ray and a refracted ray are seen together (internal reflection); at the critical angle, the refracted ray runs along the flat surface; beyond the critical angle, only the reflected ray remains (total internal reflection)
Everyday Examples
- Right-angled glass prisms use total internal reflection to redirect light through 90° or 180° in periscopes, binoculars and SLR cameras
- A diamond's high refractive index gives it a very small critical angle, so light undergoes total internal reflection repeatedly inside it, making it sparkle
- Looking up at the surface from underwater at a shallow angle, the water's surface can appear to act like a mirror, reflecting the scene below rather than showing the sky above
Total internal reflection in a right-angle prism periscope
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Refractive Index and Snell's Law
Refractive Index
- Refractive index between two media is defined as the ratio of the speeds of a wave in the two regions
- Formula:
- n = (c/v)
- Where:
- n = refractive index (no units - it is a ratio)
- c = speed of light in a vacuum (3.0 × 10^8 m/s)
- v = speed of light in the material (m/s)
- This is the special case of the general definition where the first region is a vacuum (or, to a very good approximation, air)
- A higher refractive index means light travels more slowly in that material, and bends more when entering or leaving it
| Medium | Approximate Speed of Light | Refractive Index (n) |
|---|---|---|
| Vacuum | 3.00 × 10^8 m/s | 1.00 |
| Water | 2.25 × 10^8 m/s | 1.33 |
| Glass (typical) | 2.00 × 10^8 m/s | 1.50 |
| Diamond | 1.24 × 10^8 m/s | 2.42 |
Snell's Law
- Formula:
- n = (sin i/sin r)
- Where:
- n = refractive index of the material (light entering from air)
- i = angle of incidence, in air
- r = angle of refraction, in the material
Worked Example: Using Snell's Law
Muchindu shines a ray of light from air into glass (n = 1.5) at an angle of incidence of 40°. Calculate the angle of refraction.
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