## Thursday 13 January 2011

### Physics: Optics

Optics
Light rays – a line with arrow on the line
Divergence of light ray – when we say a set of rays is parallel, they don't have intersection points; if it's converging, it'll have a intersection in front of the source (real); if it's virtual, it has a imaginary intersection point behind the source (virtual).
We observe objects when light from objects enter our eyes. Luminous object emits light so we see the object directly; wee see non-luminous object when it reflects lights into our eyes. Distant objects are assumed to be emitting/reflecting parallel light rays.
Law of reflection
1)       The incident ray, reflected ray, normal lies on the same plane.
2)       θi = θr, i.e., the angle of incidence is equal to the angle of reflection.
When the light rays are stroked on a curved mirror, the normal is perpendicular to the tangent of the curve at that point. e.g., when parallel rays are stroked on a coven mirror, they are all reflected and converge in front of the mirror.
Regular reflection occurs when the rays are reflected by a smooth surface, where the θi for all parallel rays are the same and sharp image can be formed. Diffuse reflection occurs when the rays are reflected by a rough surface, where the θi is not unique. Rays are reflected into different directions
Properties of the image: the object that we see through the mirror is not the real position of it, but we can imagine that the light rays from the object comes behind the mirror and we call that an image. They have the properties:
1)       Distance from image/object to the mirror is equal. i.e., image distance is equal to object distance.
2)       IO is perpendicular to the mirror.
3)       The image formed is laterally inverted, of the same size as the object and is virtual.
Applications: Periscope uses two plane mirror to receive image from distant position (like double-decked bus), the image is erect but not laterally inverted.
Refraction of light
Since light is a macroscopic view of EM waves, when it goes into different material, it will have different travelling speed, resulting in the refraction.
Assume the refractive index of light in vacuum is 1, where light travels in the highest speed there. The refractive index of air is almost 1 (1.0003). The refractive index of a certain medium X is given by ηX = speed of light in vacuum / speed of light in medium X.

Law of refraction:
1)       The incident ray, refracted ray, normal lies on the same plane.
2)       sin θi is proportional to sin θr
Refractive index can be also defined by ηX = sin θair / sin θX.
General form of Snell's law: η1sin θ1 = η2sin θ2.
A medium with higher refractive index is called optically denser medium, all medium are optically denser than vacuum so all medium has refractive index higher than 1.
A several phenomena can be explained by the refraction of light, like the rising of image when a glass block is placed on a plane surface, or a coin is placed into a cup of water, the real depth is different from the apparent depth.
Total internal reflection
By Snell's law, when one's refractive index is larger, there exist certain ranges of angle that the equation is not balanced. In this case total internal reflection happens.
Critical angle of medium X is given by: ηX sin c = η2sin 90˚, c = sin-1(1/ηX). It occurs when:  (1): Light ray is directed from optically denser to less dense medium; (2): θi > c
Under total internal reflection, it obeys the laws of reflection. Note that even the angle is smaller than critical angle, part of the light may still reflects, but when it exceeds the critical angle, all light rays are reflected.
Application
- Fish-eye view under the water (diver's view)
- Mirage: hot air is lower than the cold air during days, since hot air has lower density, it has a less refractive index. When light striking downwards, it has a continuous refraction, when the refractive index of a certain fraction of air is small enough, total internal reflection occur and observers can see the reflected image of the distant object on the ground, just like some water on the ground.
- Periscope by prisms: glass/Perspex prisms usually have critical angle smaller than 45˚. When two prisms are placed like plane mirrors, They can also form a periscope. Advantage: is that plane mirror in reality is composed by a thin glass layer and a reflecting layer. During reflection of plane mirror, the glass layer may produce multiple image but prisms dose not.
- Optical fibre, as well as cutting diamond in a suitable angle.
Lenses
-          Convex VS concave: convex lens is lens that is thicker in the middle part while concave lens is thinner in the middle part.
-          Cylindrical VS spherical
-          Converging VS diverging: When parallel rays pass through convex lens, they converge, when they pass through concave lens they diverge. Therefore they're called converging and diverging lens respectively.
-          Optical centre is the center of the lens
-          Principal axis passes through the optical center and perpendicular to the lens.
-          Principal focus is where parallel rays converge (or imaginary converging) when parallel rays pass through.
-          Focal length (f) is the distance between principal focus and the lens.
-          Focal plane is the plane that passes through principal axis and perpendicular to principal axis.
-          Thicker lens or lens with higher refractive index causes shorter focal length (light rays are converged in a more quicker way)
-          In the light ray diagram the figures shows the convex lens (left)and the concave lens (right).
Rules for light ray passes through lenses:
1)       Rays that passing through optical centre is not refracted.
2)       Rays that parallel to principal axis intersect or (imaginary intersection) at the principal focus. By reversibility of light, rays from principal axis is refracted to be parallel.
3)       For other rays: Firstly, construct a line parallel to the rays and passing through the optical centre. Then find the intersection between the line and the focal plane. The refracted light rays will pass through that intersection point.
The refracted image may not converge in front of the lens. Instead they virtually converge behind the lens, a virtual image is formed. Observers can still observe the image but it can't be caught by a screen.
Lens formula: 1/u + 1/v = 1/f, where u and v are object and image distance.
For f, it is positive for convex lens while negative for concave lens, v is positive when it is real while negative when it's virtual.
Linear magnification (m) = image height/object height = v/u
Nature of image formed
-          Real and inverted(v>0) VS virtual and erect (v<0)
-          Magnified (v>u or m>1), of the same size (v=u or m=1) or diminished (u>v or m<1)
Methods to determine focal length of lens:
1)       When s sharp image of a distant object is formed by a convex lens on a screen, the distance between the lens and the screen is the focal length of the lens.
2)       Attach a plane mirror to the convex lens and place them in front of an illuminated object. Move the lens-mirror combination until a sharp image is caught by the screen. The distance between the lens and the screen is the focal length of the lens.
3)       Using lens formula, obtaining different sets of (u,v), plot the graph of 1/v against 1/u (it gives y-intersection 1/f), m against v (it has y-intersection -1 and slope 1/f), v against u (intersect with line v=u at (2f,2f)).