Lenses, Visible Light and Black Body Radiation
Convex and Concave Lenses
A convex lens (converging lens) is thicker in the middle than at the edges. It bends parallel rays of light inward so they meet at a single point called the principal focus (or focal point). The distance from the centre of the lens to the principal focus is called the focal length.
A concave lens (diverging lens) is thinner in the middle than at the edges. It spreads parallel rays of light outward so they appear to come from a single point behind the lens. Concave lenses always produce virtual, upright, diminished images.
A convex lens can produce real or virtual images depending on the position of the object. A concave lens always produces a virtual, upright, diminished image regardless of object position.
To draw a ray diagram for a convex lens, you need three standard rays from the top of the object: (1) a ray parallel to the principal axis, which refracts through the principal focus on the other side; (2) a ray through the centre of the lens, which passes straight through without bending; (3) a ray through the principal focus on the near side, which refracts to become parallel to the principal axis. Where the refracted rays meet is where the image forms.
If the object is beyond twice the focal length (\(> 2F\)), the image is real, inverted and diminished. At exactly \(2F\), the image is real, inverted and the same size. Between \(F\) and \(2F\), the image is real, inverted and magnified. Inside \(F\), the image is virtual, upright and magnified (this is how a magnifying glass works).
Magnification
The magnification produced by a lens tells you how much larger or smaller the image is compared to the object:
$$\text{magnification} = \frac{\text{image height}}{\text{object height}}$$
A magnification greater than 1 means the image is larger than the object. A magnification less than 1 means the image is smaller. Magnification has no units.
Visible Light and Colour
White light is a mixture of all the colours of the visible spectrum (red, orange, yellow, green, blue, indigo, violet). When white light passes through a prism, each colour is refracted by a slightly different amount — violet is refracted the most and red the least — causing the light to spread into a spectrum. This is called dispersion.
Colour filters work by absorbing certain wavelengths and transmitting others. A red filter absorbs all colours except red, which it transmits. An opaque object appears a particular colour because it reflects that wavelength and absorbs all others. A red object in green light appears black because there is no red light to reflect.
The three primary colours of light are red, green and blue. Combining all three in equal proportions gives white light. Combining two primary colours gives a secondary colour: red + green = yellow, red + blue = magenta, green + blue = cyan. This is additive colour mixing and is used in TV and phone screens.
Colour filters and pigments use subtractive colour mixing. A cyan filter absorbs red and transmits blue and green. Placing a cyan filter and a yellow filter together absorbs both red and blue, transmitting only green.
Black Body Radiation
All objects emit and absorb thermal radiation (infrared radiation). The hotter an object, the more radiation it emits per second and the shorter the peak wavelength of the radiation. A black body is a theoretical object that absorbs all radiation that falls on it and emits a characteristic spectrum that depends only on its temperature.
As the temperature of a black body increases, the peak wavelength shifts towards shorter wavelengths (from infrared to red to white to blue). The total energy radiated per second also increases dramatically.
At room temperature, objects emit mainly infrared radiation (invisible). As they heat up, they begin to glow red (about 500°C), then orange, yellow and eventually white-hot at very high temperatures. Stars are approximate black bodies — a red star is cooler than a yellow star, which is cooler than a blue-white star.
The Earth absorbs short-wavelength radiation from the Sun (visible light and UV) and re-emits longer-wavelength infrared radiation. If the rate of absorption equals the rate of emission, the temperature remains stable. Greenhouse gases in the atmosphere absorb some of the outgoing infrared radiation and re-emit it back towards the Earth, increasing the surface temperature. This is the greenhouse effect — a natural process that makes Earth habitable, but increasing greenhouse gas concentrations are enhancing it, causing global warming.