3.1 Propagation of light
Light is a form of electromagnetic radiation that the human eye can detect, with wavelengths from about 400 nm (violet) to 700 nm (red). It travels as a transverse wave of electric and magnetic fields and needs no medium, so it crosses the vacuum of space from the Sun. In any one uniform medium it travels in straight lines, a property called rectilinear propagation, and the path it follows is drawn as a ray. Many analytical instruments, from the simple colorimeter to the UV-visible spectrophotometer, depend on sending a straight, narrow beam of light through a sample and measuring how much comes out. Example: the physics workshop of a technical training institute in Kangemi uses a pinhole camera and a ray box to show students that light travels in straight lines before they move on to spectrophotometers.
Speed of light
- In a vacuum: c = 3.0 × 10⁸ m/s (more exactly 299,792,458 m/s), the highest speed possible. Light from the Sun, 1.5 × 10¹¹ m away, takes about 500 s (just over 8 minutes) to reach the Earth.
- In materials: Light slows down in denser optical media: about 2.25 × 10⁸ m/s in water and 2.0 × 10⁸ m/s in glass. This change of speed causes refraction.
- Wave equation: c = fλ, where f is the frequency in hertz and λ is the wavelength in metres. For green light of wavelength 500 nm, f = 3.0 × 10⁸ ÷ 5.0 × 10⁻⁷ = 6.0 × 10¹⁴ Hz.
Terms used
- Luminous object: A body that produces its own light, such as the Sun, a candle flame, a lamp or an LED.
- Non-luminous object: A body seen only because it reflects light that falls on it, such as a book or a sample bottle.
- Ray: The direction of travel of light, drawn as a straight line with an arrow.
- Beam: A bundle of rays, which may be parallel (from a distant source or a collimator), converging or diverging.
- Transparent, translucent and opaque: Materials that let light through clearly (glass, water), let it through but scatter it (frosted glass, greaseproof paper), or block it (wood, metal).
Evidence for rectilinear propagation
- Three card experiment: Three cards with small holes are lined up in front of a candle. The flame can be seen only when a thread pulled through the holes is straight.
- Shadows: Opaque objects cast sharp shadows that match the straight lines drawn from the source past the edges of the object.
- Pinhole camera: A small hole in a light-proof box forms an inverted image on a translucent screen at the back.
- Eclipses: Solar and lunar eclipses happen because light from the Sun travels in straight lines and is blocked by the Moon or the Earth.
Shadows and eclipses
A point source gives a sharp shadow called the umbra, a region of total darkness. An extended source, such as a frosted lamp, gives an umbra surrounded by a partial shadow, the penumbra, where only part of the source is blocked. A total solar eclipse is seen from the umbra of the Moon's shadow and a partial eclipse from its penumbra.
The pinhole camera
The pinhole camera forms a real, inverted image. Its magnification is:
Magnification = image height ÷ object height = image distance ÷ object distance
Worked example: a tree 1.5 m tall stands 6.0 m from a pinhole camera whose screen is 0.20 m behind the pinhole. Find the height of the image.
Image height = object height × image distance ÷ object distance
Image height = 1.5 × 0.20 ÷ 6.0
Image height = 0.05 m = 5.0 cm
- Moving the screen back: The image becomes larger but dimmer.
- Making the hole larger: The image becomes brighter but blurred, because each point of the object forms a small patch instead of a point.
- Several holes: Several overlapping images are formed.
Light paths in analytical instruments
In a spectrophotometer the beam from the lamp passes through an entrance slit, is made parallel by a lens or mirror, is split into wavelengths by a grating or prism, and passes through a narrow exit slit and the sample cuvette to the detector. The path must be straight, clean and aligned, which is why cuvettes are placed the right way round, kept free of fingerprints and inserted into fixed holders.
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Create a free account 🔒3.2 Light properties
When light meets the boundary between two media it may be reflected back, transmitted and bent (refracted), or absorbed, and usually some of each happens at once. Which effect dominates depends on the surface, the two materials and the angle at which the light…
🔒3.3 Laws of reflection
The laws of reflection describe exactly where a reflected ray goes, and they apply to every reflecting surface, flat or curved, smooth or rough. For a curved or rough surface, each tiny part of the surface obeys the laws with its own normal. They are measured…
🔒3.4 Total internal reflection
Total internal reflection happens when light travelling inside an optically denser medium strikes the boundary with a less dense medium at an angle of incidence larger than the critical angle, so that all the light is reflected back and none escapes. Unlike re…
🔒3.5 Image formation by curved mirrors
A curved (spherical) mirror is a part of the surface of a sphere that has been polished and silvered. If the reflecting surface is on the inside of the curve, it is a concave (converging) mirror; if it is on the outside, it is a convex (diverging) mirror. Beca…
🔒3.6 Focal lengths, object distances, image distances and magnification calculation using mirror formula
Ray diagrams show where an image forms, but the mirror formula gives the exact position and size by calculation. It links the focal length of the mirror to the distances of the object and the image from the pole, and it is used to design reflectors, check opti…
🔒3.7 Image formation by lenses
A lens is a piece of transparent material, usually glass or plastic, with one or both surfaces curved, that forms images by refraction. A converging (convex) lens is thicker at the centre than at the edges and bends parallel rays inwards to a real focus; a div…
🔒3.8 Laws of refraction
The laws of refraction state exactly how much a ray of light bends when it passes from one medium into another. They were found by experiment by Willebrord Snell in the 17th century, and the second law is still called Snell's law. Every lens design, refractome…
🔒3.9 Focal lengths, object distances, image distances and magnification calculation using lens formula 1/f = 1/u + 1/v
The lens formula gives the position of the image formed by a thin lens from its focal length and the object distance, and so allows the size and nature of the image to be calculated without drawing. It has the same form as the mirror formula and, with the same…
🔒3.10 Refractive index, critical angle and total internal reflection
The refractive index of a material and its critical angle are two ways of describing the same property: how strongly the material slows and bends light. Once one is known, the other can be calculated, and together they tell whether light inside the material wi…
🔒3.11 Optical instruments
Optical instruments use lenses, mirrors, prisms and gratings, singly or in combination, to form images or to analyse light. Some extend human vision, letting us see objects that are too small or too far away; others, central to analytical chemistry, measure ho…
