Internal Reflection of Magnifying Glass

A few months ago, I got myself a cheap 90 mm diameter magnifying glass in a local flea market and the idea was to make a simple refracting telescope out of it. Upon inspection, I realized there was an uneven distribution of its composition which causes anisotropy in its refractive index. This defect is probably due to improper cooling rate when the glass was poured into its mould.

Other than this, both surface of this lens have non-uniform radius of curvature which translates into distortion of image it creates. Spherical aberration is also expected and can be seen from the image it produce and lastly, due to its size, chromatic aberration is very much visible and therefore this lens is of poor quality which renders (pun intended) the initial high-resolution task impossible – something I should have expected for  material that cost only RM5.

The distortion and artefacts coming out from physical defects inside the magnifying class can be seen in the picture on top; as I prepared an example how a simple magnifying glass can be used as a crude form of telescope. By putting it in front of a camera, the magnifying glass becomes the objective lens of the telescope and the lens of my camera becomes the “eyepiece”. When you have a two lens system, a telescopic image can be produced on the detector of my camera in a fashion similar to the human retina. 

We note that the tree-like object is actually a telco transmission tower disguised as a tree. The poor image quality shown here is due to the physical defects mentioned earlier and chromatic aberrations are obvious as colours are dispersed around the “branches” of the “tree” especially near to the edge of the glass.

So the cheap lens was kept in the dry box for a while until I figured out the other day of using it as a demonstration for geometrical optics: with a layer of glass and a bright beam of light made possible by commercially available DPSS green laser, it is easy to show the effect of internal reflection, where the light beam is allowed through the magnifying glass and at the interface between glass and air, the beam touches the boundary at an angle exceeding the so-called critical angle which allows it to bounce back onto another interface and so on. 

The picture above clearly demonstrated internal reflection where a beam enters the magnifying glass from the right side as evident from the relatively large green spot (saturated by scattered light upon entrance into the glass) compared to other bright spots on the glass. This ray of light is then reflected inside the glass upon the glass-air boundary until the 6th order where the thickness of the magnifying glass is thinning upon the edge (think of the shape of a magnifying glass) and the internal reflection finally lost its critical angle upon the interface.

Although we can increase the number of times the beam gets reflected inside the lens, it should be noted that this kind of reflection has its loss mechanisms. That is the intensity of light after each reflection suffers reduction in its “brightness” due to transmission towards outside of the glass-air interface. The next picture illustrates how:

Six green streaks of light on the wall came from the bright points on the magnifying glass shows some part of the light gets out of the magnifying glass (instead of being internally reflected) and hit the wall at the back. The central hyperbolic-shaped shadow corresponds to the black opaque plastic which holds the magnifying glass. Notice the loss of light intensity is obvious as the brightness of the spots decreases when we count from left-bottom spot to right then to left again all the way up. In some ways, we can see each reflection point inside the magnifying glass is similar to the interface of a beam splitter where some parts of the light is being reflected into the interface and some being allowed to let through. 

Nonetheless, it should be noted that internal reflection is only applicable when the wave (in our case: in a beam of light) travel from a medium with a higher refractive index (in our case: the magnifying glass) to another medium (in our case: air) with a lower refractive index, and precisely because of this, internal reflection of waves found many applications in our life. 

One good example is the use of fibre optics in telecommunications, where digital signals are compressed in a form of light pulses and then sent into a sort of "pipe" that is made of glass or other transparent materials having a higher refractive index compared to its surrounding. This enable the light signals to internally reflect along the fiber which essentially behaves like a "light-conducting" cable, transporting important scientific signals or streaming YouTube videos across the continent. 

In the regards of use in architecture, the brilliant application of internal reflection manifested in light tubes like this. It is useful to reduce energy requirements for lighting (because natural lighting is dirt cheap if you don't consider the cost of light tube), thus making homes, offices or public buildings more environment friendly.

*  *  *

Back to the demonstration: So previously, I placed the lens vertically on a wooden board allowing a beam of light coming from an adjustable plane. Now, assuming the optical axis of the magnifying glass were placed vertically parallel to the z-axis on the y-plane, introducing a beam of light from negative x, y, z axis towards the edge of the lens produced a fantastic internal reflection pattern where reflection order of 10 and above is observed and the path of reflection was bent according to the curvature of the lens. I reckon this reflecting configuration should have its practicality as a waveguide but I haven’t any idea where and how it should be used yet. 

Anyway, when the angle of incidence is adjusted carefully, the internal reflections take place in a ringed configuration suggesting the importance of curved surface geometry to the reflecting beam. Despite the appearance of high reflection order, we note the reflection spot in orders from 10 and above (at the top of the magnifying glass) starts to decay into a featureless smudge. 

Any good guess why?

Moiré and Carbon Atoms

Here is one example of an optical phenomena coming from a common kitchen object, when briefly examined, I am surprised at the remarkable resemblance with something I've come across while attending microscopy lectures not too long ago. 

Figure 1

Anyway, this is a demonstration of Moiré pattern using a metallic teapot filter. If we pay attention to our surrounding, Moiré patterns are actually quite common! It is an intereference pattern caused by two grids overlaid at different grid size or orientation angle. This effect is the easiest to find when we cross two thin fabric over a bright light source. Try doing it! 

What I have, as mentioned, is a metallic filter that comes in cheap teapots. It has an arranged structure (like wire gauze or weaving of a thin linen) forming a mesh of individual holes with diameter not more than 0.5 mm. I used a white L.E.D as light source, trying to illuminate this object from various angle and capture the result Moiré pattern with my digital camera. 

Figure 2

The pattern itself is obvious even without specific lighting. But when we started to manipulate the light source, we can see how the contrast changes which are essentially reciprocal to each other. i.e. white change to black, vice-versa. 

Comparing figure 1 and 2, the patterns are reciprocal, albeit at a slightly different superperiod (superperiod is defined as the distance from one end of a repeating Moiré unit to another). Apparently the superperiod are affected by the camera's focal ratio and the distance of the teapot filter to the camera. I haven't yet explore this variable but I believe I would come back to that some day when I have a flat Moiré pattern generating object (like two pieces of transparency film with parallel lines) instead of a cylindrical (more accurately, a circular conical section) holey filter I'm using now. 

Anyway, you can say this Moiré pattern was generated by two superimposed mesh of pinholes. The pinholes are uniform in size so it is the tilt angle that creates this pattern.

Hence, from the superperiod, D, of the imposed pattern, we can estimate the angle of tilt, Z, following a few quantities such as the diameter of the pinhole, d, by this expression:

D = d / [2 sin(Z/2)]

From figure 1, we note that the superperiod is about 7 times the diameter of the pinholes. i.e. D ≈ 7d. So putting this into the equation above, should give us Z ≈ 8 degrees. Now, how do we verify this? 

Because the Moiré pattern was formed by superimposing symmetrical pinholes around a conic section,  which means the pattern is formed by overlaying the front and back part of a "cylinder", the angle of the cone can represent the angle of tilt of the pinhole mesh. 

Figure 3

Figure 3 shows the image of my teapot filter. By measuring the diameter of the bottom and the top of the conical section and the height of the filter, we are able to use simple geometry to calculate the angle of the cone, which roughly correspond to the angle of orientation tilt of the pinholes.

What I got, was 6.1 ± 0.9 degrees, taking account into the uncertainty of measuring all the parameters. So, comparing this result to the estimated tilt angle, well, it doesn't coincide perfectly but we see comparable results under forgivable error. After all, the superperiod was based on estimation of pinhole diameter without actual physical measurement. 

Anyway, what was important, is because this Moiré pattern was formed by circular pinholes, any physical phenomena that is caused by superimposing two grids of circles with identical diameter should yield the same Moiré pattern.

And that is precisely what I found in an article from the Cambridge Nanoscience Centre. According to the article, graphite (the thing that made pencil write on papers) which are made of stacks of one-atom-thick sheets of carbon (graphene) weakly "stick" to each other, can dislocate and slide from one another fairly easily. Because atoms are spherical (simply speaking), so when we see these superimposing sheets of atoms under special microscope (Scanning Tunneling Microscope) it will show interesting Moiré pattern, formed by the carbon atoms themselves! 

Figure 4

I mean, look at figure 4! When I photograph the demonstration, I used a L.E.D to cast a shadow of my teapot filter on the wall and the Moiré pattern emerged (left) matches so well with the Moiré pattern coming from overlaying two sheets of graphene that was seen using specialized microscopes (right). 

Now I'll never see my my teapot filter the same again - if at all, after I have broke the glass teapot itself which render its filter useless other than the purpose of novel photography. 

Father of all science?

Last week, a friend of mine suggested doing a debate as a ‘performance’ on the welcoming night for us first years in the faculty, and the title suggested by him was “which is the father of all science? Physics, Chemistry or Biology?” I think there is quite a lot to say about it.


Obviously, I’d say the father of all science is obviously Physics as compared to the other two options which are chemistry and biology respectively.


Why physics? How is physics the father of all science?


The way I perceive it, physics deals with the laws that govern the entire universe – from the smallest atomic scale to the huge cosmological scale. Physics gives the theory and the equations that explain how everything works with precise mathematical details that were developed by many brilliant physicist and theorists since centuries ago.


Chemistry on the other hand is the synthesis of physics. It was developed from the ideas of physics, notably the atomic model that describes the bonding of electrons in all of chemical reactions. Ever heard of physical or radio chemistry? All this intricate knowledge of chemistry is derived from the discovery in nature that was explained by physics. The Pauli Exclusion Principle which postulates the spin properties of electrons, the energy levels for understanding thermo-chemistry and the electron shells (s,p,d,f that stands for Sharp, Principle, Diffuse, Fundamental) that predicts the probable location of electrons in an atom are derived from the wave functions in quantum mechanics – all of them are fundamentally related to pure physics.


What about biology?


Biology is in turn, explained by chemistry. The complex life as we know it is quite simply made up of tiny pieces of cells. I’m no biologist, but as far as I know, the cells run their daily lives with all the necessities that are organic chemical compounds. They generate energy via glucose (for example) which is a form of organic compound. The DNA, is a chemical compound. The pheromone, dubbed the potion of love, is also an organic compound. All of these complex interactions inside any living being are basically chemistry at work.


This whole idea is called the “physics first” movement that was proposed by particle physicist, Leon M. Lederman. He discovered the muon neutrino in 1962 and the bottom quark in 1977. Won Nobel prize in physics for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino.


So... Who is the father of all science?

A little thing about waves

Adapted from Wikimedia. Translated and edited by myself.

The red curvy line is a representation of wave.

All the other components are noted down.

The period of the wave (wave period) is usually denoted as the symbol T.

The wavelength is usually denoted with the greek letter lambda (λ).

The frequency of a wave is given by the formula:

Where the symbol f is the frequency.

*Note that frequency is the reciprocal of the wave period.*

The unit for frequency is Hertz. (Hz)

In short, the shorter the wavelength means higher frequency (more waves in a second) and if the wavelength is longer, it means it has less waves in a second.

For musicians,they see frequency as pitch. Everytime when they play a tone, it reprisents a note with a specific frequency. For example:

Start with the middle C in piano, and it goes C, D, E, F, G, A, B, C. This is called an octave. As you press the keys starting from the middle C to the next adjacent keys, you are actually listening to the a note with a higher frequency each time you press it.

So, each time you press the adjacent keys, all you hear is the note with a higher pitch.

Click here for a more details about waves. (high school level)

What's matter about?

So, let's start from the basics in order to understand what popular science books was telling all about superstrings, hyperspace and black holes.


First of all, we have to understand what is matter.

In physics, everything in the universe is classified into 2 very broad categories.

I. Matter
II. Energy

Matter, is simply anything in the universe that has mass. So, all object we touch or see is made up of matter. Water is made up of matter, same for iron, birds, mountains, humans and the stars.

Energy however is basically the thing that moves matter or contained in it.

Now, if you see the observable universe, you'll realise matter can be classified into a few categories. Mainly into 3 types. (there are actually more than that, the Bose-Einstein condensate and plasma are the extra two)

I. Solid
II.Liquid
III.Gas


Solid ice, liquid water, gaseous steam (cloud)


For example, water has 3 states of matter. Each state is called a phase. Ice, liquid water and steam. Each phase can exist under a certain temperature and pressure. That is, the amount of energy that the water molecules possesses.


The phase diagram of water.
Horizontal axis - Temperature
Vertical axis - Pressure


Matter is made up of tiny particles we called atoms. For solid, the atoms are arranged in a lattice and the atoms vibrate without moving apart. Whereas in liquid phase, the atoms have enough energy to move around and for gaseous phase, the energy contained inside the atoms are great so they move in the container fast, bouncing into each other and the container itself.


So, what are atoms made of?


From high school, we know an atom has a nucleus and the nucleus are made up of protons and neutrons. The nucleus are surrounded be electrons moving in their respective 'orbits'.

Now, thanks to the advent of particle collider and high energy physics, we know that protons and neutrons consist of even tinier particles we called quarks.



Generally speaking, matter is what we see, touch and smell everyday and it has five states of matter. Namely; the Bose-Einstein condensate, Solid, Liquid, Gas and Plasma. All of them are made up of atoms and the atoms are made up of smaller constituents.