Lens

The power of the lens equal to reciprocated of the focal length in meter or 100/f for focal length in cm (unit : dioptri/ diopter)
Convex Lenses
Thicker in the center than edges, lens that converges (brings together) light rays.
There are 3 kinds of convex lenses : plan(o)convex, biconvex and concav(o)convex
Concave Lenses
Lens that is thicker at the edges, diverges light rays. There are 3 kinds of concave lenses plan(o)concave, biconcave and convex(o)concave

Ray tracing for convex lens

Ray #1: Light ray comes from top of object; travels parallel to principal axis will be refracted thru focal point.
Ray #2: Light ray comes from top through center of lens is undeviated.
Ray #3 : Light ray comes to the focal point will be refracted to the principal axis
Special for convex lens, we can categorized 5 zone of object and image which simplify us to know the characteristics of the image:
1. Object in zone 1 (from the lens to the focal point) will create image in zone 4 (at the same zone as the object) which means virtual, magnified and upright
2. Object in zone 2 (from the focal point to the 2 times of focal point) will create image in zone 3 (from the 2 times of focal point or more) which means real, magnified and upside down
3. Object in zone 3 (from the 2 times of focal point or more) will create image in zone 2 (from the focal point to the 2 times of focal point ) which means real, reduced and upside down
4. Object in the focal point will create infinity image
5. Object in the two times of focal point will create the image at the same place which means real, same size and upside down.

Concave lens and its ray tracing

Ray #1: Light ray comes from top of object will travelparallel to principal axis will be refracted, as if it comes from the focal point.
Ray #2 : Light ray comes from top of object travels through center of lens will be undeviated.
Ray #3 : Light ray to the focal point will be refracted parallel to the principal axis.

Now compare your ray diagram with below formula

where f for the focal length, s for the distance of the object and s1 for the distance of the image. Do not forget to value virtual image and virtual focal point as a negative value. Then you will find the same result of calculation and diagram. For the magnification you can find by dividing the image distance with object distance or image height with object height.

Lens Exercise
1. Draw the ray diagram when an object was placed in front of convex lens at zone 1
2. Draw the ray diagram when an object was placed in front of convex lens at zone 2
3. Draw the ray diagram when an object was placed in front of convex lens at zone 3
4. Draw the ray diagram when an object was placed in front of convex lens at focal point.
5. Draw the ray diagram when an object was placed in front of concave lens at zone 1
6. Draw the ray diagram when an object was placed in front of concave lens at zone 2
7. Draw the ray diagram when an object was placed in front of concave lens at zone 3
8. Draw the ray diagram when an object was placed in front of concave lens at focal point.

Optical Instruments

Optical Instrument

Eyes
Eyes are convex lens because they have to create real image to hit the retina so that we will be able to see objects. To see distant object, the lens will become thinner hence to see close object, the lens will become thicker, thus enable the object to be placed in zone 3 to create a reduced image in our retina.
Our eyes are able to see object or virtual image.
To see how the light comes to our eyes, visit :
http://www.ziddu.com/download/4536270/Howlightcomestoeye.pps.html

Optical instruments can be categorized into 2 types that is connected to eyes or other medium. The one which is connected to eyes should create a virtual images because our eyes only receives virtual images. Consequently, the one which is connected to medium should create real images.

Here are the examples that created virtual images:


Concave Lens
Nearsightedness (myopia) can not see distant object, to help them, we use diverging lens because diverging lens will make distant object become closer object. Their eyeball is too long, image focuses in front of retina. It will expand the focal length so the image will be focused in retina.

Convex Lens
Farsightedness can not see near object, to help them, converging lens is needed to make a further image that can be seen by farsightedness. Their eyeball is too short, image focuses behind retina. Convex lenses shorten the focal length. It also helps presbyopia which eyeball is too short because of age, image focuses behind retina

Cylindrical lenses
It is used to help astigmatism – irregular curvature of retina so image is blurred
Cylindrical lenses reduce the irregular to focus the object

Telescope
Telescope is used for seeing distant object. Virtual image should be formed in front of the telescope so that we will be able to see the object. Telescope contains at least 2 lens, one is used for the objective lens (near to the object) and the other for eyepiece (near to our eyes). The focal length of the objective lens should be bigger than the eyepiece due to the object distance. Therefore, the power of lens of the objective lens is smaller than the eyepiece.
Normally for the objective lens, the converging lens is used to converge all the light, to make a clearer image.
When the light of the distant object comes to objective lens, the image will be formed on the focal point of the objective lens. he created image will be an object for the eyepiece.
Eyepiece can be made by using both convex or concave lens, because both lens will create virtual images. However the concave lens will diminish the object, which will make us hard to see the object.
To create virtual images in a convex lens, object should be placed below focal point, this will lead to the maximum length of telescope as an addition of focal length of objective lens and eyepiece.
To create virtual images in a concave lens, object can be placed anywhere however the results are varied but in general is reduced image.
The magnification of a telescope can be calculated as focal length of an objective lens over focal length of an eyepiece.
Meanwhile, the maximum distance of a telescope is an addition of focal length of objective lens and eyepiece.


Microscope
Microscope is used for magnifying tiny object. Virtual image should be formed in front of the microscope so that we will be able to see the object. Microscope contains at least 2 lens, one is used for the objective lens (near to the object) and the other for eyepiece (near to our eyes). The focal length of the objective lens should be smaller than the eyepiece due to the object distance. Therefore, the power of lens of the objective lens is bigger than the eyepiece.
The lens that is used for microscope is convex lens, because the main idea of microscope is to magnify object, which only can be done by convex lens.
For a maximum magnification of microscope, the object in front of objective lens should be placed in zone 2 (so it will create a real and bigger image in zone 3 for the eyepiece). Then, the object for the eyepiece should be placed in zone 1 so that a virtual and magnified image will be formed.
Magnification of a microscope can be calculated as a result of magnification of objective lens times by magnification of the eyepiece.


Magnifying Glasses
Magnifying glasses or loupe is used for magnifying object. Virtual and magnified image should be formed, that's why convex lens is used.

Examples that create real images are:
Camera
The principle of camera is the same as eye because the image should be made at the back of the lens (real image). In that case, camera should use converging lens (convex). The object should be put over 2F because film / negative in camera can handle a reduced image not a magnified image. The further the object, the focal length of the camera should be longer too (we can achieve this by reducing the power of camera lens or forwarding the lens to the object). The real image will be projected to photographic paper or camera screen which enable us to see a picture. It can be used to magnify the image too.

Diascope / projector
Created image is real and magnified.

Photocopy machine
Created image is real and same size, however it can be used to magnify and reduce objects too, depends on the position of the lens. To magnify means we place the object in zone 2, hence, to have a reduced image, we should place the object in zone 3, etc.

Matter and Atom

All matter is made up of elements.
There are 92 elements that occur naturally. The elements hydrogen, carbon, nitrogen and oxygen are the elements that make up most living organisms.
Matter has mass and takes up space.
Atoms are basic building blocks of matter, and cannot be chemically subdivided by ordinary means.The word atom is derived from the Greek word which means indivisible.
Atoms are composed of three type of particles: protons, neutrons, and electron. Both the protons and neutrons reside in the nucleus.
Protons is positive charge, neutrons have no charge and electrons (reside in orbitals around the nucleus) is negative charge.
Protons and neutrons are responsible for the atomic mass (mass number) while the number of protons determines the atomic number.
To know the atomic number and mass number, we can check from periodic table, for example 6C12 means the atomic number is 6 (it has 6 protons), mass number is 12 (it has 6 neutrons).
For exercise : find atomic number and mass number of Freon, Helium, Oxygen, Barium.

The number of protons in an element is constant (e.g. Hydrogen only has 1 proton) but neutron number may vary, which will lead to varied mass number. When the same element may contain varying numbers of neutrons (mass number) ; these forms of an element are called isotopes. Carbon, with atomic number of 6 can have 6, 7, or 8 neutrons (Carbon 12, Carbon 13, Carbon 14)
The chemical properties of isotopes are the same, although the physical properties of some isotopes may be different. Some isotopes are radioactive, they "radiate" energy as they decay to a more stable form.

A condition of which the number of neutron are the same for two elements (which have different atomic number) are called isotones. For example Boron 12 and Carbon 13

When mass number of two elements are equal, we called these elements as isobar. For example Boron 12 and Carbon 12.

Exercise : find isotopes, isotones and isobar of Barium and Calsium

A compound is a stable neutral group of at least two element in a strong bonding.
An ion is an atom or compound which has lost or gained one or more electron.
A mixture is a stable neutral group of at least two atoms or compound in a weak bonding that can separate easily (mostly by physical action).

Exercise : which one molecule, compound, ion, mixture of following :
1. Water
2. Alcohol
3. Acetone
4. Syrop
5. Juice
6. Acetic acid
7. Urea (fertilizer)
8. Urine
9. Cheese
10. Cake

Atomic bond is a strong bond that can not be separated unless a chemical action occurs. There are 2 kinds of atomic bond :
* Ionic bond is a bonding for a positive charged ion to a negative charged ion (usually a bonding consists of metal and nonmetal element, e.g. salt / NaCl)
* Covalent bond is a bonding for nonmetal element e.g. water

Exercise : which one the ionic bond and covalent bond
1. Salt
2. Acid
3. Amonium
4. Lactic acid
5. Nitrogen Compound
6. Base
7. Sugar
8. Rhizobium

Physical changes due to pressure and temperature which will result as a changing of texture, shape, size, color, mass, weight, and density without disturbing the bonding of the components.
Physical changes are reversible, means after they occurred, they can change to the former condition, e.g. shaping log into toys

Physical processes that were trigged by pressure are:
* Filtration uses some apparatus such as filter (paper) and tunnel e.g. to separate sand from seawater
* Injection e.g. to form plastics bead into plastics tray
* Chromatography is a separation of stationary components by moving the other components to other direction e.g. to separate black into its components
* Sedimentation takes a longer time to settle all the bigger density material e.g. water sedimentation from the sand and other deposits
* Centrifugation takes a short time because of the rapid centrifugal force e.g. to separate blood cell from its plasma by centrifuge

Kind of physical processes that were trigged by temperature are :
* Evaporation e.g. to separate salt from salt solution
* Crystallization use heat to separate due to the difference of the boiling point e.g. to crystallize candy
* Distillation use heat to separate due to the difference of the boiling point e.g. to separate kerosene from oil

Chemical changes due to pressure, temperature etc and will lead to changing of bonding. This changes can be observed as a result in gas (bubble), sound (explosion), odor, heat, form (burning), precipitate, decomposition of components.
Chemical changes are irreversible, means after they occurred, they can not be changed, e.g. fermentation of cassava will create lactic acid.

Refraction

Simple refraction or bending of light can be observed by watching the apparent depth of a pool is shallower than its depth.
When light comes to the different medium, the light will be bent.
When light from less dense media come to more dense (denser) media, the light will be bent approaching the normal line ( i > r ).
When light from denser (more dense) media come to less dense media, the light will be bent away from the normal line ( i < r )

Law of Refraction
1.The incident ray (i), normal and the refracted ray (r) all lie in the same plane.
2.For two particular media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant (sin i/sin r = constant = n =refractive index) or mathematically
n1 sin i = n2 sin r
1 refers to where the incidence ray comes and 2 refers to where the refracted ray comes.
The refracted index for air, usually taken as 1

Refractive index also can be calculated as V air / V medium
When we see through a pool, its depth will look shallower, by knowing its refractive index, we can calculate the apparent depth as n = real depth / apparent depth

Work Example of Refraction

State whether this statement true or false
1. The light comes from the air to the water can be bent up to 30 degree depends on the angle of incidence.
2. The light comes from the denser medium to the less dense medium will be bent away from the normal line.
3. The shining diamond occurs because refraction.
4. Total internal reflection only occurs when the angle of refraction is bigger than critical angle.
5. Rainbow is a sample of dispersion due to different medium of light transmission during rain
6. Calculate and sketch the ray from air to plastics (refractive index 1.5) as below
7. If the incident ray comes with the frequency of 1014 Hz then find the frequency, wavelength and speed of the refracted ray

Total Internal Reflection
When the light travels from the denser medium to a less dense medium, the light will be bent away from the normal line. As the angle of incidence is increased further, it will reach the critical angle ( angle of incidence which will create angle of refraction value as 90 degree ). Consequently, when the incidence light reach over the critical angle, total internal reflection will occur. For example, by taking the normal critical angle of a glass is 41 degree, we can know that when the angle of incidence light less than or equal to 41 degree,refraction will occur, on the contrary, total internal reflection will due. Observe the figure below from left to the right, when the angle of incidence is 30 degree(less than its critical angle), the light will be refracted away from the normal line. When angle of incidence equal to critical angle, the light will be refracted as far as 90 degree. Last, when the angle of incidence is 45 degree (more than its critical angle), the light will be reflected inside the medium (total internal reflection).

Total internal reflection can be seen in a optics cable, the benefit of using total internal reflection is that it will transmit quickly and clearly.

Saturday, 10 January 2009

Light and Mirror

What is Light?
As atoms absorb energy, electrons jump out to a higher energy level.
Electrons release light when falling down to the lower energy level.
Photons - bundles/packets of energy released when the electrons fall.
Light as stream of photons

Color of Light
1. Transparent Objects
Light transmitted because of no scattering
Color transmitted is color you see. All other colors are absorbed.
2. Translucent
Light is scattered and transmitted some.
3. Opaque
Light is either reflected or absorbed. Color of opaque objects is color it reflects.
White light is the presence of ALL the colors of the visible spectrum.
Black objects absorb ALL the colors and no light is reflected back.

Light and its Sources
Luminous object
Luminous objects have their own light example : sun, firefly, light worm
Hence, non luminous objects reflect light example : moon, hand
Incandescent light
Light produced by heating an object until it glows.
Fluorescent Light
Light produced by electron bombardment of gas molecules
Phosphors absorb photons that are created when mercury gas gets zapped with electrons. The phosphors glow & produce light.
Neon light
Neon inside glass tubes makes red light.
Other gases make other colors.

Reflection of Light

Reflection – Bouncing back of light waves at the same angle (angle of incident = angle of reflection or α = β) and same plane. The green dashed line is showing the normal line to help us identify the angle of incident (the angle between the incident ray and the normal line) and the angle of reflection (the angle between the reflection ray and the normal line), the normal line should be perpendicular to the plane.
Kind of reflection :
1. Regular reflection – mirrors smooth surfaces scatter light very little. Images are clear & exact. 2. Diffuse reflection – reflected light is scattered due to an irregular surface.

Exercise :
1. Draw the reflection of the light when a light enter at the angle of 20 to the plane
2. Draw the reflection of the light when a light enter at the angle of 45 to the normal line

Term of Image / Shadow
Real Image - Can be projected onto a screen because light actually passes through the point where the image appears , always inverted
Virtual Image - “Not Real” because it cannot be projected, image only seems to be there
Upright – Image' position is the same as the object
Inverted – Image is upside down.
Laterally inverted – Image is right side left
Enlarged – Image is larger than actual object.
Reduced / Diminished – Image is smaller than object.
Converge / Converging – Bring the light to a point








Diverge / Diverging – Diverge the light to many points.










Principal Axis – Base line through the center of a mirror or lens
Focal Point – Point where reflected or refracted rays meet & image is formed
Focal Length – Distance between center of mirror/lens and focal point
Centre Point – Centre point of a mirror or lens

Plane Mirror – Perfectly flat
Image is virtual, laterally inverted
An angled mirror will create number of shadows as (360 / α) – 1 where α is the angle. For example two mirrors when placed to create an angle of 90 will give us 3 shadows

Convex Mirror (Diverging Mirror)
- Curves outward, virtual focal point.
Image is virtual, laterally inverted, reduced, upright, closer than it appears
Use: Rear view mirrors, store security

Ray #1: Light ray comes from top of object will travel parallel to principal axis is reflected as if it come from focal point.
Ray #2 : Light ray comes from top of object to the center of mirror will be reflected back.
Ray #3 : Light ray comes to the focal point will be reflected to the principal axis
Exercise :
Find the image and its characteristics by drawing and calculating in front of convex mirror with the centre point of 5 cm when the object is placed
(1) 8 cm in front of the mirror
(2) 3 cm in front of the mirror
(3) 1 cm in front of the mirror

Concave Mirror (Converging Mirror)
Curves inward, real focal point.

Ray #1: Light ray comes from top of object will travel parallel to principal axis will be reflected to focal point.
Ray #2 : Light ray comes from top of object travels through center of mirror will be reflected back.
Ray #3 : Light ray comes to the focal point will be reflected parallel to the principal axis
Exercise :
Find the image and its characteristics by drawing and calculating in front of concave mirror with the centre point of 5 cm when the object is placed
(1) 8 cm in front of the mirror
(2) at the centre point of the mirror
(3) 3 cm in front of the mirror
(4) at the focal point of the mirror
(5) 1 cm in front of the mirror
If your drawing is right, you will find the characteristics as (1) real, inverted and reduced (2) real, inverted and same size (3) real, inverted and magnified (4) infinity image (5) virtual, upright and magnified

Therefore we can conclude, special for concave mirror, we can categorized 5 zone of object and image which simplify us to know the characteristics of the image:
1. Object in zone 1 (from the mirror to the focal point) will create image in zone 4 (at the back of the mirror) which means virtual, magnified and upright
2. Object in zone 2 (from the focal point to the centre point) will create image in zone 3 (further than its centre point) which means real, magnified and upside down
3. Object in zone 3 (further than its centre point) will create image in zone 2 (from the focal point to the centre point ) which means real, reduced and upside down
4. Object in the focal point will create infinity image
5. Object in the centre point will create the image at the same place which means real, same size and upside down.

Now compare your drawing (the place of your image) with the formula:
1/f = 1/s + 1/s’ where f is focal length and s is distance of the object and s’ is distance of the image
M = h’/h = s’/s where M is magnification and h is height of the object and h' is the height of te image. When magnified, the value of M is more than 1. Then if it is reduced the value is less than 1. Last, if the value of M is 1, it means that the image has a same size as its object.
Both should show the same place, or it means that there is something wrong with your drawing or calculation.


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