July 29, 2010 · 7:50 pm

Should literacy include science?

Today I have an article inThe Irish Times, the Irish newspaper of record. It is the first of a series of commissioned articles on science and society. Basically, I make the point that if Newton and Boyle were to come back today, they would be astonished at the progress science has made but dismayed at the fact that this knowledge is restricted to so few. This is a great pity for two reasons

(i) the great discoveries of science are an important part of the human experience

(ii) a great many of the challenges facing modern society involve an understanding of basic science, and more importantly, how science is done.

I’m constantly amazed at the way expert scientific opinion is drowned out in media debates by those who know nothing of the subject, from discussions of nuclear power to climate change. But is this any real surprise if neither journalists nor the public have any knowlege of the painstaking, self-correcting methods of science? Ons solution might be that science form a basic part of every child’s education.

You can read the article on the Irish Times website or here if that link is closed

Update

There was a program on climate on TV3 last night that illustrates the point exactly: a 50/50 tv debate between 2 scientists and 2 members of a pressure group who knew nothing of the subject and repeated every well-known canard imaginable…utterly depressing

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July 21, 2010 · 7:33 pm

Enigma and Katyn Forest

Wow. Caught the movie ‘Enigma’ again on tv last Sunday night. I knew the story, but Id forgotten just how good it was. I  enjoyed the film so much I bought the book on Monday in order to re-read it. What did I discover? I hadn’t read the book at all. Oh joy!

Robert Harris is an superb historical novelist and this has to be his masterpiece. Superbly written, well-informed, a fantastic plot – it simply has everything. Even the love angle is utterly convincing. As for the maths – the description of the codebreakers and their methods is superb. I think the description of the loneliness of the mathematican is the best I’ve ever come across.

Most important of all, the story just rushes along. It basically concerns the famous work at Bletchley Park in WWII, as the best and the brightest of Britain struggle desperately to break the Navy, Luftwaffe and Werhrmacht codes using a combination of guesswork and an early computer. The hero of the book is young mathematician Tom Jericho, which I presume is a stand-in for computer genius Alan Turing. Every now and then, the German ‘weather book’ changes, and they’re back to zero. The description of the codebreaking is superb, as is the serious subplot – when the Allies evesdrop on German reports of the Russian Katyn forest massacre, a British codebreaker of Polish origin decides he doesn’t want to be allied with Russia and attempts to leak the codebreaking secrets to the Germans. Clever plot – perhaps it really happened?

Apart from a great plot, it’s good to see codebreaking get recognition it deserves. Just last week, I read an article on the Battle of Britian that ignored the role of science, as usual.Yes, the pilots were brave – but important advances in both code-breaking and radar also gave the Britian an edge in that vital battle..

A  super read and a super introduction to the world of computing. Go and get it now.

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July 8, 2010 · 5:00 pm

What are you doing for the summer?

What are you doing for the summer? Like most academics, I get asked this question every day in summer, usually by people who are convinced that college gates are locked the day students finish their exams.

Actually, that’s partly true. Some lecturers in the Institutes of Technology take off on June 20th and reappear on September 1st; as is their right, given the heavy teaching load during termtime. However, for those of us who try to keep up the research, the summer months are the time to get something done.

A few years ago, I used to spend my summers at my alma mater Trinity College, doing experimental work in the physics department. These days, I find myself doing more and more writing for the public about science, from particle physics to cosmology. Truth is, I always liked writing more than toiling in the lab..

This summer, I am reading up on climate science. I taught an introductory course in climate change last semester and found it utterly fascinating. It is a hugely challenging, multidiscpinary area of science that is firmly rooted in basic physics. Also, for anyone with an interest in the Public Understanding of Science, climate change certainly the hot topic; in no other field of science is there such a gap between what scientists believe (I should say what the vast majority of scientists in the field believe) and what the public believes – more on this later.

It’s great to finally have the time to sit down and read all the material, from the latest reports of the Intergovernmental Panel on Climate Change to recent research by groups at the Goddard Institute for Space Studies or the Hadley Centre for Climate Research. However, I am not reading up on the material just for fun – I’m frantically preparing for a year at the Science, Technology and Society Program of the Kennedy School of Government at Harvard University. Yes, I have been invited to spend next year at Harvard – don’t ask how I managed this!  My particular research topic will concern the science of climate change and the root causes of climate scepticism, so I’d better know my stuff.

Of course I won’t spend the entire summer on preparation for Harvard. I do a few hours work at home most mornings, walk into the village for lunch, and then spend the afternoons at WIT printing out papers and studying etc. Most days after work, I’ll have a long cycle and a swim, or an occasional game of tennis, so it’s not a hard life!

In August, I’ll spend 10 mad days at my favourite music festival, the Festival Interceltique de Lorient. After that, I intend hole up somewhere where I can surf in the mornings, work in the afternoons and play tunes  in the evenings – probably Doolin. And then it’s Harvard in September yipee!

Great session In Lorient last year

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July 1, 2010 · 3:48 pm

Climate change: a burning question on tv

This week, RTE (the national broadcasting authority of Ireland) aired a program on climate change. ‘A burning question‘ was an hour-long TV documentary on climate science, climate scepticism and the role of the media in this debate. The program was produced by Earth Horizon Productions, directed by Paula Kehoe and edited by Dónal Ó Céilleachair. I watched the program out of general interest and was intrigued to see my name listed in the credits (I think this arose from several discussions I had with Dónal).

I thought the program very good overall, with some reservations. It’s hard to cover such a topic in an hour, so the producers employed some media tricks that few scientists enjoy. I’m not sure cutting to a vox pop every few minutes throughout the program casts much light on the subject matter (besides, are the opinions of random individuals stopped on the street a reliable gauge of the view of the general poulation?). Secondly, the constant switching from expert to expert in a cyclic merry-go-round of byte-sized interviews tends to confuse rather than elucidate. Thirdly, I thought the program could have had more on climate skepticism (see below).

That said, the core of the program was solid. The main presenter was Duncan Stewart, an award-winning architect and environmentalist well-known for his excellent TV series Eco-Eye. There were some very good interviews, notably with heavy hitters such as former UN High Commision Mary Robinson, UN Secretary General Ban Ki-Moon and IPCC Chairman RK Pachauri.

Duncan Stewart of Earth Horizon Productions

The key scientist of the program was superb; Peter Lynch, a leading climatologist at University College Dublin, gave the lie to the old media adage that experts make poor communicators. Professor Lynch explained the basic principles of the enhanced greenhouse effect in exemplary fashion, starting with the work of pioneers such as Fourier, Tyndall and Arrhenius, and finishing with modern measurements of carbon dioxide emissions and surface temperatures. Interesting that the best way to explain science is often to describe it in chronological order of discovery!

Prof Peter Lynch of UCD

There were many other good contributions in the program; in particular from the environmental writer John Gibbons (on the societal impacts of climate), from Professor John Sweeney (Professor of Geography at UC Maynooth and member of the IPCC) and from economist and boadcaster David McWilliams (on the economics of climate change). One of the most lucid summaries was given by former UN High Commisioner Mary Robinson – describing the expected impacts of climate change on the poorest societies in the world, and the importance but difficulty of concerted international action, she left one wishing other politicians had as good a grasp of the subject.

Prof Mary Robinson, former UN High Comissioner

Justin Lewis, a Professor of Journalism and Media Studies at Cardiff University, talked a little about the role of the media in the public perception of climate science. He explained the basic problem clearly; that in the media’s attempt to present a balanced debate view, the observer is left with the impression of a great 50/50 debate between experts, rather than the overwhelming consensus that exists. This is the familiar problem of a ‘balanced debate’ in the media that pays no attention to weightings. Lewis also touched on ‘climategate’, contrasting the great publicity afforded to the hacked East Anglia emails with the minimal media attention given to the results of the subsequent enquiry (the ‘perpetrators’ have since been exonerated).

Prof Justin Lewis of Cardiff University

I thought this section very interesting, but there could have been more: for example, there was no mention of the obvious point that “Scientists Right!” is not much of a media story, while “Scientists Wrong!” is. By definition, the minority viewpoint will always get more publicity, a fact the public should be made aware of. I also thought that more time could have been spent on the analysis of the role of journalists. Given the dominance of the media in our lives, this is a key issue in the pubic perception of science (and of anything else). In particular, there was no mention of the issue of political bias. Much of the climate scepticism in the US media is driven not by business interests, but by journalists of a particular political viewpoint: the viewpoint of right-wing conservatives who oppose government regulation and taxation in all forms.

In general, I thought the program could have had more on climate skepticism, rather than simply dismissing it as ‘vested interest’. In my opinion, there are at least five distinct categories of skepticism (with many overlaps):

(i) A tiny minority of genuine scientists with no links to industry or politics (such as Freeman Dyson or Richard Lindzen), who remain unconvinced of the scale or extent of man-made warming. Such minority opinion is important, but exists for almost every scientific theory (an obvious fact that is almost never stated in the media).

(ii) A larger group of economists, political scientists and intellectuals such as Bjorn Lomborg who remain unconvinced. This community are strong on economics but they are not scientists and rarely understand the reliability (and limitations) of experimental measurements – another fact that is rarely highlighted in the media.

(iii)A huge community of commentators, journalists and bloggers who seem to have almost no appreciation of the difference between random, informed, and expert opinion. A great deal of these reject the opinion of the majority of scientists as biased and subscribe to all sorts of ‘rent-seeker’ conspiracy theories.

(iv)The vested interests of big business; as in the case of the tobacco lobby, there are still climate scientists who are paid to believe what they believe

(v)The political viewpoint of conservatives and anti-regulation interests; I suspect this last sector is much more influential than is generally realised.

Overall, I enjoyed the program very much – it’s hard to cover everything in one hour. I nearly fell off the couch when I saw my name in the credits!

Update

Justin Lewis has a book out on climate science and the media – ‘Climate Change and the Media’ looks well worth a read

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June 23, 2010 · 8:48 pm

The sound of music at the LHC

The BBC have a great story about a new way of searching for the Higgs boson (or God particle) using sonic modelling; each layer of energy in a particle detector is represented by a note and their pitch is different depending on the amount of energy that is deposited in that layer. By analyzing the resulting sounds, it’s possible that physicists may be able to pick out the Higgs particle by “listening to the data”. You can hear a sample of what the Higgs might sound like on the BBC website.

Simulated collision event producing a Higgs boson

Richard Dobson, a composer involved with the project, says he is struck at how musical the products of the collisions sound – “We can hear clear structures in the sound, almost as if they had been composed. They seem to tell a little story all to themselves. They’re so dynamic and shifting all the time, it does sound like a lot of the music that you hear in contemporary composition”.

Actually, that doesn’t surprise me . Most good music is pleasant to the ear because of internal symmetries. Given that our understanding of particle physics is founded on elegant mathematical symmetries, it’s not surprising that if you translate particle masses and energies into sound you get pleasing sounds!

Best of all, this might offer another way to seach for brand new particles  – I wonder what supersymmetric particles would sound like?

Update

Musicians wanted – CERN, Switzerland

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June 16, 2010 · 3:15 pm

‘Black Holes, the Hadron Collider and the God Particle’

We got a massive turnout on Monday evening for a public lecture I gave on the Large Hadron Collider at Trinity College Dublin. I was invited to give the talk by Astronomy Ireland and it was a great time to give it as there is still plenty of interest in the Collider because of the black hole ‘controversy’, and because last week saw the first offical conference on results from the LHC. Indeed, there has been very little media attention given to the fact that, in the space of a few months,  all four detectors at the LHC have been busily rediscovering the elementary particles of the Standard Model that took so many years to first detect, from pions, muons and kaons right up to W and Z bosons.

A lot of physicists might have a problem with the populist title ‘Black holes, the Hadron Collider and the God particle’; however the title was worked out with Astronomy Ireland, an organisation that knows a thing or two about attracting a wide audience! Also, I think controversies such as the black hole controversy are best tackled head on i.e. by describing early on in the talk what a black hole is and why one doesn’t expect to create one at the LHC  (in particle physics, one gets only a minute amount of mass  from a very large amount of energy since  m = E/c2 ). I also touched on micro-black holes and Hawking radiation; overall I had the distinct feeling the audience enjoyed this part of the talk no end!

As for the term ‘God particle’, I happen to be one of the few physicists who likes this name for the Higgs boson. Yes, it was probably originally ‘that goddamn particle’ due to its elusiveness,  but I think ‘God particle’ neatly gets across the importance of the particle; after all it is the interaction of the other particles with the Higgs field that is thought to determine their mass, according to the Standard Model.

I divided the talk into three parts; first, an overview of the LHC – how, what, why etc. Then I devoted the central part to a brief history of particle physics, from the discovery of the nucleus to protons and neutrons, from the hypothesis of quarks to the electroweak interaction and the Standard Model. In the third part, I described extensions to the SM such as supersymmetry and Grand Unified Theory and went over our expectations of the LHC experiments, from the possible detection of the Higgs boson to supersymmetric particles, from candidates for dark matter to the search for assymetries in matter/antimatter decay at LHCb.

The LHCb experiment is of particular interest to an Irish audience, as a group at University College Dublin are heavily involved, despite Ireland’s non-membership of CERN.

Finally, I can never resist showing a couple of slides on the basics; not only do experiments at accelerators give us information on the elemental structre of matter and the interaction of the fundamental forces, they also give us supporting evidence for our underlying theories of modern physics, from the observed mass-increase of particles (predicted by special relativity) to the detection of antiparticles (predicted by quantum theory). You can see the full set of slides for the talk here and a video is available here.

All in all, there was a great atmosphere at the talk and I really enjoyed the occasion. There were plenty of questions afterwards, from queries on black holes to the prospect of detecting extra dimensions. I was also asked about a recent study of the cosmic microwave background (CMB) that may cast doubt on the hypothesis of dark matter (based on a revision of measurements of perturbations in the  CMB). I haven’t studied this report yet, but I gave the answer that I always give in public fora: let’s see if other groups replicate the findings before pay too much attention. After all, the postulate of dark matter comes not primarily from measurements of the CMB, but from thousands of measurements of the movement of stars, galaxies, galaxy-clusters and halos. That said, it’s certainly an interesting paper…

Update

I really enjoy giving such talks on particle physics, there are so many fascinating subjects to cover; special relativity, quantum theory, quarks, the fundamental interactions, symmetry breaking, antimatter, dark matter etc. Yet while there are quite a few excellent books for the public on cosmology, there are remarkably few on particles physics… might be fun to try to put one together one day.

Update II

Apparently, U.S. newspapers are full of stories on the discovery of the God particle at the Tevatron. It seems these stories are based on an unpublished paper (see discussion on Not Even Wrong) – I wouldn’t pay too much attention just yet.

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June 3, 2010 · 10:13 pm

Genius of Britain; Dawkins vs Hawking

This week Channel 4 have been running a superb series on British science and scientists, from the 17th century up to the present. It was a beautifully produced, meticulous piece of television, with mini-biographies of British scientists down through the ages, narrated by well-known scientists such as Stephen Hawking, Richard Dawkins, Jim Al-Khalili and David Attenborough.

Each night covered a different century, with scientists like Hooke, Wren, Boyle, Halley and Newton in the first episode,  and Crick, Watson, Hoyle (with a link to Hawking’s work)  and Hamilton (with a link to Dawkin’s work) in the last. In between, one got to hear about other great, less-recognized scientists, such as Watt, Maxwell, Rutherford and Turing.

All in all, it was a superb series, truly inspirational, with a great balance between the sciences. I thought the chronological approach worked really well in general. Of course, the nationalistic angle made nonsense of the story at times; one kept wondering why a crucial step was left out, then you remembered that this was not the story of science, but of British science; a strange angle from a scientist’s point of view.

This might explain a few flaws here and there; for example, I thought the discussion of Fred Hoyle quite odd. Instead of discussing Hoyle’s major contribution to cosmology ( the carbon step in nucleosynthesis), narrator Jim Al -Khalili concentrated on Hoyle’s ‘steady-state’ theory of the universe. This reverence for Hoyle’s theory is baffling to non-British scientists; steady-state made very little impact in the world of science outside of Britain (despite huge media interest in Britain) and proved to be comprehensively at variance with the evidence.

In the last part of the program, Richard Dawkins made the point that science is not undamentally about math, or experiments, but about asking questions. There ensued a fascinating short discussion between Dawkins and Hawking on the big questions.

Richard Dawkins  and Stephen Hawking in conversation

“What really happened before the Bang?” Dawkins asked Hawking.  Hawking gave the standard, simple response – there is no before because time is part of the universe, as predicted by general relativity (he seemed surprised by the question, as was I).

Hawking had a far harder question for Dawkins:

“Why are you obsessed with God?” It is exactly what I would have asked, but Dawkins seemed quite taken aback by the question. He responded initially by claiming that Stephen had brought up the question first, with his famous last line of A Brief History of Time (‘..for then we shall know the mind of God’), which isn’t much of an answer. However, Richard then said that his main problem with religion is that religious explanations for nature are a distraction from the real path of finding out have things work.. fair comment!

Update

It seems a book based on the series is already available..more on the series here

The Irish Times reviewed the series in their weekend review; sadly, it wasn’t a very good piece, focusing almost exclusively on the fact that Robert Boyle was Irish not British. A fair point, but where was the rest of the review?

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May 20, 2010 · 8:40 pm

Science v humanities: a matter of presentation?

I attended two very different seminars in college today and the differences were striking.

The first seminar was titled ‘Academic Freedom and the Notion of Rights’, and was given by a visiting lecturer in philosophy. He talked for an hour on the subject of rights, perceived rights, fundamental vs non-fundamental rights etc …and in the last ten minutes touched on the issue of academic freedom within this context. Basically, it was a long and detailed talk without any visual aids on the philosophy of human rights, with a little bit on academic freedom thrown in at the end.

(The talk was followed by a response, a much shorter talk by the Technology Transfer Officer at our college. This speaker gave a short, pointed talk on the concept of academic freedom, using several well-known cases in the news as examples. I liked this talk better, but again it was hard to make out the central point of the argument and there was no attempt to elucidate points with diagrams, pictures or slides).

After lunch, I attended a very different talk ; a seminar on recent research into gene therapy in plants by Prof. Liam Dolan, Sherardian Professor of Botany, University of Oxford. Now, I know as much about plants as you do about astrophysics, but the lecture was clear, well-laid out and easy to follow. The speaker made great use of simple pictures and excellent overheads, and explained the basic concepts of his field and the relevance of his research to society in exemplary fashion. At no stage were we bombarded with information, yet I came away knowing  good deal more than when I arrived. You can see the abstract for Liam’s talk here.

So there is the difference. One speaker renders an obscure, complex subject simple by presenting it in a clear, coherent manner – another presents an interesting, relatively simple topic in convoluted terms, rendering it far more complicated than necessary. Could it be that scientists tend to be clear because they have to be?  The subject is difficult enough as it is and swiftly becomes impenetrable  if not clearly explained.

Update

A colleague has suggested that ” we may have become used to visuals and it can be a challenge to listen attentively for 40 minutes”. It’s a fair point but I didn’t feel challenged. In fact, I think the narrative style allowed the speaker to repeat himself at regular intervals in a way that would become much more obvious if visual aids had been used!

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April 23, 2010 · 11:35 am

Introductory physics: the photoelectric effect

One of the last lectures in an introductory physics course is usually a description of the photoelectric effect. This is because the effect is a beautiful manifestation of one of the astonishing discoveries of modern physics; that light, known to behave as an electromagnetic wave, can in some circumstances behave as a stream of discrete particles.

The first hint of this dual nature of light arose from Planck’s study of blackbody radiation in 1900 (see post on radiation). Planck found that he could only predict the observed spectrum of radiation from a hot body if it was assumed that the radiation was transferred between the body and the walls of a container in tiny, discrete packets or quanta of energy, each quantum having an amount of energy given by E = hf ; here f is the frequency of the radiation and h is a fundamental constant of nature (extremely small) that became known as Planck’s constant.

This assumption was regarded as something of a puzzling mathematical trick until a young Einstein suggested in a famous paper that it was the light itself (as opposed to some transfer process) that was quantized i.e. the blackbody spectrum could be described by assuming that light was behaving like a stream of extremely small, discrete bundles of energy, each of energy E = hf. This was a bold assumption as the wave properties of light were well established, but Einstein backed up the idea by showing it explained several other puzzling phenomena, not least the photoelectric effect.

The photoelectric effect was a well-known phenomenon whereby light incident on a metal could cause electrons to be released by the metal (measurable as an electric current). A great puzzle was that the effect ocurred only for light above a certain frequency, characteristic of the metal under investigation; this result was completely inexplicable in terms of the familiar wave theory of light.

Light of a certain frequency incident on a metal causes a current to flow

Einstein showed that the photoelectric effect could be easily explained if the incoming light was behaving as a stream of discrete packets (or photons) of energy. Invoking the conservation of energy, he predicted that the maximum kinetic energy (K.E.) of electrons liberated from the metal would be given by

K.E.e =  hf  –  W0

where each incoming photon of light has an energy of hf and W0 is the binding energy (or work function) of the metal. Clearly, electrons could be released from the metal only if the incoming light was of a frequency such that hf  >  W0 , irrespective of the intensity of the radiation! Could it be that simple? The experimentalist Phillipe Lenard disliked Einstein’s idea intensely and set about disproving it in a series of experiments; years of careful experimentation showed that Einstein’s theory was exactly right in its predictions (see here for more details).

Experimental measurement of the photoelectric effect: no electrons are emitted below the cut-off frequency

The explanation of the photoelectric effect was a significant breakthrough in physics as it represented the first unequivocal evidence of duality; the phenomenon whereby light can behave as a wave in some situations and as a stream of particles (or quanta of energy) in others. This duality formed a cornerstone of the new quantum theory and was later found to be a universal truth of the microworld –  entities known as  ‘particles’ such as electrons and even atoms were in turn found to exhibit wave behaviour.  Indeed, the quantum equation E = hf is as important in modern physics as E = mc2 and it was for his explanation for the photoelectric effect (not for special or general relativity) that Einstein was awarded the 1921 Nobel Prize in physics.

Historical note

Philosophers and journalists often claim that ‘Einstein disliked quantum theory’. It should be clear from the above that Einstein was one of the major pioneers of quantum physics; his view of quanta of light was far ahead of its time and was at first strongly resisted by the scientific establishment (including Planck). What Einstein disliked was a later interpretation of quantum theory known as the Copenhagen interpretation, a view of the quantum world that is still debated today.

Excercise

If light of wavelength 780 nm is incident on sodium metal (work function of 3.6 x 10-19 J), calculate the maximum kinetic energy of emerging electrons. (Hint: recall that wavelength and frequency are related by c = fλ and note that h = 6.6 x 10-34 Js )

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April 15, 2010 · 4:42 pm

Introductory physics: the lens

A spectacular application of the phenomenon of refraction (see previous post) is the lens. Just as a focusing mirror is used to obtain an image of a distant object (see post on mirrors), a lens is used to focus light by refraction. The difference is that the light is transmitted through a lens – it is refracted once entering the lens and again as it passes out again. Lenses are cut from parabolic surfaces in such a way that distant rays are brought to a focus at the focal point.

As with mirrors, there are two types of lenses, depending on the curvature of cut: a convex lens causes parallel rays of light to converge to a real focus, while a concave lens cause the light to appear to diverge from a virtual focus.

As with mirrors, the position of an image will depend on the distance of the object from the lens (but the image of a distant object will of course be at the focal point of the lens). Amazingly, the same equation applies: for an object a distance u from a lens of focal length f, the location v of the image can be found from the relation

1/u +  1/v =   1/f

(Note that for a distant object u = ∞ and hence v = f ). The magnification m of the image can be calcuated from the equation m =  –v/u, as before.

Applications

Lenses are used extensively in everyday life. The most common example is of course spectacles. No one knows when spectacles were first invented (12th century?), but they have been used throughout the ages to improve defective human eyesight.

Typically, spectacle lenses are concave (diverging) lenses are made from glass or plastic. This is because the most common eyesight defect is myopia (shortsightedness), a condition where the natural lens of the eye focuses too strongly i.e. an image is formed short of the retina. A diverging lens of the right strength placed in front of the eye will cause the image to be projected back on the retina as normal.

Concave (diverging) lens used to correct myopia

In the case of hyperopia (the longsightedness that occurs commonly in older people), the eye muscles are weakened and an image is formed beyond the retina; this is corrected by placing a convex (converging) lens in front of the eye in order to strengthen it i.e. shorten the focal length of the eye’s natural lens.

Converging lens used to correct longsightedness

A modern application is the contact lens: this operates on the same principle as above, but the lens is made of a soft fabric that can be worn directly on the pupil. A third option nowadays is laser surgery; in this case the focal length of the eye’s natural lens is adjusted directly (and permanently) by laser treatment.

Lenses and science

Lenses played a pivotal role in the development of science. In the 17th century, advances in lens technology led directly to the invention of the microscope, a device that revolutionized our view of the world of the very small: and to the development of the telescope, an invention that revolutionized our view of the solar system and ultimately the entire universe.

Exercises

1. If an object 5 cm high is placed 30 cm in front of a convex (converging) lens of focal length 20 cm, calculate the position and height of the image.  Is the image real or virtual?

2. As a shortsighted person ages, can the onset of longsightedness cancel myopia?

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