Monthly Archives: June 2012

What is a ‘Retina’ display?

Apple describes some of its products as featuring a “Retina” display. But what does that actually mean?

The individual pixels (each one made up of three red, green and blue subpixels) that make up my laptop’s display, viewed through a magnifier.

The main claim that Apple makes of its Retina display is that the pixels used are so small that they are too small to be seen individually by the human eye. In physics terms, this means that these pixels are below the resolving power of the human eye.

The resolving power of the human eye is about 60 arcseconds, or 0.0167 degrees. This means that any two objects separated by an angle smaller than this will appear as one object to the eye. The minimum vertical or horizontal spacing between two items which are visible as separate items is therefore given by dtan(θ) where d is the distance to the items and θ is the resolving power of the eye.

Assuming that the display in question is held or viewed at a distance of 30 cm from the eye, this distance is found to be 0.0873 millimetres. This means that a person with normal vision will be able to discern individual pixels on any display with fewer than 11.5 pixels per millimetre.

As can be seen from the graph above, the screen of the iPhone 4 does possess a greater density of pixels than the human eye can perceive; but the iPad 3 and the just-released 2012 MacBook Pro do not. (None of this matters of course, because “Retina” is just a trademark that Apple uses as a marketing term.)

An argument could be made, in the case of the MacBook Pro, that the distance between the screen and the eye would usually be larger than 30 cm. If the distance was 50 cm that would make the resolution of the eye 6.88 pixels per millimetre and therefore give the 2012 MacBook Pro a “true” retina display.

An astonishing photograph

At the recent Institute of Physics Teachers’ Group AGM, Anu Ohja from the National Space Centre in Leicester drew our attention to this incredible photograph of the Apollo Lunar Module returning to dock with the Command/Service Module.

The amazing thing about this photograph is that it contains all of humanity with the exception of one person.

Everybody alive, except for Michael Collins, who took the photograph, appears in this photograph: the entire population of Earth, plus Neil Armstrong and Buzz Aldrin aboard the Apollo LM.

Human beings have more than five senses

Traditionally human beings are traditionally said to possess five senses: sight (vision), hearing (audition), touch (tactition), taste (gustation) and smell (olfaction).

But you have many more senses that aren’t included in the list above.

You have a sense of balance* (equilibrioception) because your ear contains three semicircular “canals”, two of which are oriented at right angles to each other and the third which is at a 30° angle to the others. When the head moves in the x, y and z planes (i.e. roll, pitch and yaw) the liquid (endolymph) contained in these canals lags slightly behind. This causes hair cells (cilia) contained in a vessel at the end of the canal to bend and this sends a signal down the vestibular nerve to the brain. If you spin around and then stop the liquid continues to move for a short while and the confusing signals the brain receives is what causes dizziness.

Your sense of pain (nociception) is not, as many people think, connected to your sense of touch. Special sensors called nociceptors, located in the skin, the lining of bones and elsewhere react to certain types of stimuli. Once the stimuli reaches a given point (the “pain threshold”) a signal of varying strength (depending on the stimuli) is sent to the brain via the spinal column. The reason that you instinctively grab an injured body part is that there is only so much bandwidth available in your nervous system to send signals to the brain, and when you grab something there is less room for pain signals as the body needs to make room for the touch signals.

You are able to sense temperature (thermoception) because of specialised sensors in the skin called thermoreceptors that detect the movement of thermal energy. You also have a different type of thermoreceptor in the hypothalamus of the brain that detect the body’s internal temperature and regulate sweating, shivering, etc.

Your sense of the passage of time (chronoception) isn’t controlled by a specific part of the brain, but is thought to be as a result of the interaction of the cerebral cortex, cerebellum and basal ganglia in the brain. Another part of the brain, the suprachiasmatic nucleus, is responsible for controlling your circadian rhythms, the daily cycle of body temperature, blood pressure, wakefulness, sleep, etc. One of the main inputs (zeitgebers) that controls the body’s circadian rhythms is the presence or absence of sunlight.

If you close your eyes you are still able to touch the tip of your nose because of your sense of proprioception: the sense of where your body parts are located relevant to each other. This connects with your vision to provide eye-hand coordination.

Your body constantly monitors the amount of oxygen and carbon dioxide in the brain using chemical sensors in the brain called peripheral chemoreceptors which provide a sense of suffocation if these percentages get too high.

You also have a number of senses that detect stimuli within the body: chemoreceptors in the body monitor salinity and create a sensation of thirst when levels are too high†, and sensory receptors also provide sensations when swallowing or vomiting and which control the body’s gag reflex. The chemoreceptor trigger zone in the brainstem’s medulla oblongata monitors drugs and hormones in the blood and induces vomiting when necessary, for example during food or alcohol poisoning. There are also receptors in the bladder and bowels that control the need to excrete waste and stretch receptors in the stomach and intestines that sense distension due to the presence of excess gas.

There are also a number of senses that humans do not possess, but which are possessed by other living things.

Bats, dolphins and some other animals use echolocation to sense the position of objects by measuring the reflection of sound waves from those objects. Some profoundly blind humans have also been suggested to possess this sense.

Some aquatic animals, most notably fish, have a sense of electroreception that enables them to sense electricity and to navigate by using the fact that water conducts electricity and other substances (rocks, riverbeds) do not. No land-bourne animals are known to possess this sense which is unsurprising considering how poorly air conducts electricity.

Magnetoception is the ability to detect magnetic fields that is possessed by some bacteria and which is thought to allow insects (such as honeybees), birds and other animals (e.g. turtles, stingrays) to navigate.

Some insects have the ability to use the polarisation of light to navigate and spiders have slit sensillae in their exoskeletons that detect strain, enabling them to detect forces and vibrations in their webs. Plants are also able to detect the direction of gravity, enabling them to grow upwards towards light sources.

* Your sense of balance is also responsible for your sense of acceleration and for your ability to know which way is down (i.e. which way the gravitational field points at your location).

† These sensors also provide a sense of thirst in diabetics when sugar levels are too high.


I am not really an astronomer or an astrophysicist (my expertise and interest is in the areas of nuclear and particle physics) but I will make an exception for the constellation of Cassiopeia.

The term “constellation” refers to a region of sky, so the constellation of Cassiopeia technically contains hundreds of stars, but what most people think of as Cassiopeia is the stretched ‘W’ shape made by the five brightest stars.

Alpha Cassiopeiae (α Cas, Schedar) is a cool (4500 K) orange giant star located 229 light-years from Earth. It is the brightest of the stars in Cassiopeia.

Beta Cassiopeiae (β Cas, Caph) is a warm (7100 K) yellow-white giant variable binary star 54.5 light-years from Earth. It is the second brightest of the stars in Cassiopeia and varies in apparent magnitude (brightness) between +2.25 to +2.31.

Gamma Cassiopeiae (γ Cas, Tsih) is a hot (31 000 K) blue subgiant eruptive variable binary star, the prototype of the shell type of variable stars. It is by far the most powerful of the stars in Cassiopeia but only the third brightest* as it is located 613 light-years from Earth. Gus Grissom, an astronaut who took part in Mercury and Gemini missions and who died in the Apollo 1 accident named the star “Navi”, after his middle name backwards, as the star was commonly used as a navigational aid during space missions.

Delta Cassiopeiae (δ Cas, Ruchbah) is a warm (8400 K) blue-white star, part of an eclipsing binary system. It is located 99.4 light-years from Earth.

Epsilon Cassiopeiae (ε Cas, Segin) is a hot (15 200 K) blue-white giant star and is the dimmest of the five, at a distance of 442 light-years from Earth.

Cassiopeia also contains some other interesting stuff: ρ Cassiopeiae and V509 Cassiopeiae are yellow hypergiants and two of the most luminous stars in the Milky Way, with ρ Cas being more than ninety million times the size of the Sun and around half a million times more powerful. Cassiopeia A is a the remnant of a supernova that occurred 300 years ago and the brightest source of radio waves outside of our own Sun. Cassiopeia also contains the Pacman nebula and two Messier objects, M52 and M103, both of which are open clusters visible from Earth with binoculars.

* The brightness of γ Cas varies irregularly but when it is at its brightest, with an apparent magntiude of +3.40, it is the brightest star in Cassiopeia.