Refraction occurs when a light ray travels from one medium (substance) to another.
Refraction happens because mediums have different densities, so the light does not travel at the same speed. The light travels through air quicker than it does through glass, for example.
Refraction only occurs if the light hits the boundary at an angle, because, as the image shows, one side of the light ray hits the boundary before the other.
A lens adds curvature to a wave as it passes through.
When waves are uncurved before passing through the lens, and it is parallel to the lens axis, the waves will be given a spherical curvature, centred on the focal point of the lens.
Lenses can curve the wavefronts by slowing down the light travelling through the middle of the lens for a longer time than the light at the edges of the lens. This means that all the points on the wavefront take the same amount of time to get to the focus point
The focal length is the distance between the lens axis and the focus.
The more powerful the lens, the more strongly it will curve the wavefronts, so the shorter the focal length will be.
Refractive index = speed of light in a vacuum/speed of light in medium
Refractive index is a ratio, so it has no units.
Power = 1/focal length
Power is in dioptres (D) and focal length is in metres (m).
Curvature = 1/radius of curvature
The amount of curvature a lens adds to a wave is 1/f, which is just the power of the lens.
1/v = 1/u + 1/f where v is the distance from the lens to the image, u is the distance from the object to the lens, and f is the focal length.
v, u, and f have to be in metres (m).
Magnification = size of image/size of object
Magnification is a ratio so it has no units.
Examples of using lens equations
The object is at a large distance. What is the curvature?
1/u = 0. So 1/v = 0 + 1/f. Therefore the lens will give it a curvature of 1/f.
The image is 80cm away from a 3.25D lens. What is the distance from the object to the lens?
Power = 1/f = 3.25D
v = 80cm = 0.8m
1/u = 1/v - 1/f
1/u = 1/0.8 - 3.25
1/u = -2
u = -1/2m, so te image must be 0.5 metres from the lens.
magnification = size of image/size of object.
The image is 26*14m. The object is 13*7m.
What is the magnification?
26/12 = 2 OR 14/7 = 2
The magnification is 4.5. The size of the image is 27*45m.
What is the size of the object?
27/4.5 = 6m AND 45/4.5 = 10m
Size of object: 6*10m.