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H.1.1

Diffuse and specular reflection...Specular reflection is like in mirrors where an image is formed as a result. This is caused by very smooth surfaces, which reflect light back out evenly across their entire surface. Diffuse reflection is the more common example of light bouncing of anything else to form an image of that object (ie when light bounces off a piece of paper, we see the paper not a reflection). This is caused by the fact that the surface of the paper is not smooth, but rather light is reflected in all directions (look at a mirror form different angles and you see different reflections...the paper looks the same from all angles. Diffuse reflection is what allows us to see things, since otherwise we could only see objects emitting light...but as it is we can see everything which isn't pitch black (ie absorbs all light)...when there's enough light around that is :)

H.1.2

Formation of virtual images in plane mirrors...Light travels out in every direction form every point on the object, but it's impossible to draw them all, so a ray diagram is used. It is usual to have the object as an arrow on a slope, pointing up (though anything which will show both rotation and inversion will be sufficient). Draw tow rays form a point, slightly diverging (separating) which then strike the mirror, and then reflecting (angle of refraction = angle of incidence...draw a line perpendicular to the mirror, the angel of entry one one side equals the angle of exit on the other). These two lines then move away form the mirror and react the 'eye'...just draw something to represent it, it isn't an art contest :) The two rays reaching the eye are then extended back up 'inside' the mirror to the point where they meet (should be on the same level as the original object)...this is where the image is formed...upright, 'flipped' around a vertical axis, and a virtual image). Draw the image inside the mirror.

H.1.3

Mirrors are used in optical instruments mostly to let us see things which aren't actually in front of us (or viable normally). Bike mirrors allow us to see the car about to run us down...periscopes allow submarines to see, and then blow up ships on the surface. Cristina suggests the mirror on the moon was used to measure it's distance form earth, but bouncing a laser off it, and measuring the time for it to return...this seems plausible, but you'd have to be able to measure the time very accurately, because it would be very short.

H.1.4 : Lots of definitions

Radius of curvature - if the curve of a lens was extended into a full circle, the radius of curvature is the radius of the circle. It is only relevant for spherical lenses, but they're the only ones we consider anyway. The focal length of a spherical mirror will be half the radius of curvature, or the radius of curvature will be 2F, which ever way you want to look at it.

Principle axis - the principle axis is defined as a line perpendicular to the curved surface of the lens at its center...ie - a line running horizontally through the center of the lens.

Principle focus - related to the focal length of the lens... ie - one focal length away from the center of the lens (therefore there are two principle foci, one on either side, usually designated F on the far side, and F' on the same side as the object.) Parallel rays of light entering the lens either converge towards the principle focus (convex lenses) or diverge from it (concave lenses).

Focal length - Focal length is the shortest distance between the principle axis and the principle focus.

Paraxial rays - Paraxial rays are those that are close to the principle axis and parallel to it.

Magnification - the magnification is usually defined as image height/object height, representing in effect how much bigger the image is. This is also be directly related to image distance/object distance.

H.1.5

A virtual image is defined as one which doesn't actually have any light rays running through it, only 'virtual' rays (ie the ones extended inside the mirror). Real images are those which do have light rays running through them (those which can be shown on a screen)...As for drawing ray diagrams to help analyze this, I suppose that falls under the 'if light rays go through it' definition. Real images are generally used in projection systems, where the image is being displayed on a screen (or cast directly into the eye). Virtual images are often used, for example, in magnifying lenses, where the image must be viable from different angles.

H.1.6

The mirror equation...this equation is

.

So based on two of image distance, object distance and focal length, the third can be found. This equation is in the data book under the Optics section.

H.1.7

Thin lenses are used to converge or diverge light within optical systems. Telescopes, for example, focus the light from stars onto our eyes, at the end of the telescope, and magnifying glasses diverge the light, forming a magnified virtual image on the other side.

Thanks to Blazej Zak for this info --

Acoustic lenses -- An acoustic lens focuses sound in much the same way that an optical lens focuses light. Snell's law describes the refraction of sound as it passes through an interface between two materials of differing sound speed. An acoustic lens provides the appropriate material thicknesses that focus a parallel wavefront of sound to a single focal point.

Microwave lenses are presumably something to do with microwaves...which are really just another part of the em spectrum, so they will do the exact same thing with lenses as viable light...I suppose in microwave ovens you use diverging lenses to scatter the microwaves around...but if anyone can elaborate...

Drawing ray diagrams...First draw in the principle axis, and the lens (convex or concave as appropriate) in the center. Mark points on the principle axis on both sides for the focal point and 2x the focal point (F and 2F). Draw the object (again usually an arrow) on the left. Draw two rays from the top of the arrow. The first runs parallel to the principle axis until it hits the lens, then goes in a straight line down through the focal point (for a convex lens) or goes in a straight line away for the focal point on the object's side (for a concave lens). The second ray runs from the top of the object to the center of the lens, where it meets the principle axis, and continues straight through. If these two rays meet on the other side, then this is where the image will be formed (ie where you should put the screen) if they diverge, then trace both line back from the lens to where they meet on the other side...this forms a virtual image on the same side as the object, which must be viewed without a screen form the opposite side of the lens. If the object was on the focal point, then the two rays will be parallel, and no image will be formed.

The sign conventions -- Basically, heights above the principle axis are positive, below are negative. The focal length of a converging lens is considered positive, and diverging positive. The object distance is positive if it is on the same side as the light is coming from (almost always the case) and the image distance is positive if it is on the opposite side to where the the light is coming form (in general, positive for real images, negative for virtual).

H.1.8 : Deriving the lens equation

This is done using the similar triangles formed by the ray passing through the center of the lens. ( #1 is formed by the object, the principle axis and this ray, #2 is formed by the image, the principle axis and the ray). This allows us to get the relationship:

, since all sides of the triangles are in proportion. The second pair of triangles are formed by the ray going down form the the lens through the focal point (as in drawing the diags). This forms a triangle #1 with the lens (height is equal to Ho), the axis and the ray. Tri #2 is the image, the axis and the ray.

This allows us to get the relationship:

.

Nb, the top term is for a diverging lens, but this is eliminated because is negative. These two equations can then be equated and simplified to form

, the lens equation...(yes, it's the same as the mirror equation). This is much clearer with diagrams...I'll get round to them someday. As can be seen also from the first equation, Di and Do are also directly related to the ratio of heights...ie the magnification.

.

H.1.9 : Some optical devices

Simple magnifier (ie a magnifying glass)...This uses a convex lens, where the object is placed closer than F to the lens. This results in a magnified, virtual image behind the lens (actually further than the object, but it's bigger to compensate). This allows the object to appear bigger than it is...ie -- read words in small print etc.

Compound microscope...Produces a magnified, upside down image by using two lenses. The first lens, close to the object, is called the objective, while the second is called the eyepiece. The object is place further than Fobjective away form the objective lens. This then converges the light to form an image closer than Feye piece to the eyepiece lens. this results in the light diverging out of the eyepiece, and so by tracing back we can find the position of the magnified virtual image.

Astronomical telescope...This is virtually identical to a compound microscope, except this time the light is entering not form an object, but in parallel lines at an angle to the lens (since it is coming from so far away). The objective lens focuses the light at a point closer than Fe which then diverges it, and forms a magnified, upside down image behind the lens.

H.1.10 : Total internal reflection prisms and optical fibers

(this bit will eventually be moved to 11.1.4, but it's here until I do that bit)

Total internal reflection (TIR)...Total internal refraction is a result of snell's law, when the angle of refraction is greater than 90. Light is traveling in a substance when it meets a boundary with a less dense medium on the other side. As a result, the light will be refracted away from the normal. There comes a point, however, where the resulting refraction is 90. SinØc = n2/n1. Since sin90 = 1, it can be canceled out. if the angle of incidence is equal to Øc, then the light will travel along the surface of the more dense medium. if it is greater, however, then all the light is reflected back into the more dense medium.

TIR prisms...When light traveling inside a prism reaches a boundary and attempts to leave, it is subject to total internal reflection, if the angle of incidence is greater than Øc. As such, a (right angle triangular) prism can be designed where Light enters on the vertical side, is totally internally reflected against the hypotenuse, and then leaves through the bottom side. This can be used to form a sort of periscope without using mirrors, which means 100% of the light is transmitted (mirrors tend to lose some). Also, such a prism could be designed so, when placed with it's hypotenuse down, light entered one side and was refracted downward, TIRs on the bottom side and then leaves the other side. This means that rays entering the prism higher up, come out further down (because they strike the bottom further along). This can be used, therefore, to invert an image...ie in the telescope described above.

Optical fibers...Optical fibers consist basically of a very thin 'wire' of a material with a high refractive index, into which light is sent. Since it has a high index, even when the fiber is bent, the critical angle will still not be exceeded, and all light will be totally internally reflected. This can then be used to transmit light very easily around corners etc, and since the light travels very quickly without resistance, it is preferable to using electric current in wires, and so can be used in telecommunications. These fibers can also be used to carry light into the human body, and also, as in an endoscope, to allow us to examine the inside of the human body without cutting it open ( or doing any other gross biology stuff :). Decorative lamps are a rather trivial use...but you can use them for that to.

Nb...In the first two applications, is is important that fibers next to each other are optically insulated, so no light can possibly jump from one to another. This is usually done by coating them in a material of lower refractive index than the fiber.

H.1.11

Ithink I vaguely remember something about this, but I'll have to go digging through some old notes...anyone want to help out?

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