Before you read this, I suggest you read post 22.4. The electrons in an atom can scatter x-rays because they move up and down as the electric vector of the x-rays oscillates, as describe in post 22.4. So, the moving electron is a simple harmonic oscillator if the x-ray wave is a sine wave. The… Continue reading 22.15 X-ray scattering by an atom

Before you read this, I suggest you read post 19.20. In post 22.13, we saw that we couldn’t use a microscope to find the positions of atoms in molecules. But, in principle, we should be able to obtain some information from an x-ray diffraction pattern. This post gives more details. X-rays are scattered by the… Continue reading 22.14 X-ray diffraction

Before you read this, I suggest you read post 22.12. In post 22.12, we saw that, in the microscope, the first stage of image formation was formation of a diffraction pattern in a plane that I have labelled the diffraction plane. Waves then continued to form an image, so that the image of point A… Continue reading 22.13 Resolution of the microscope

Before you read this, I suggest you read posts 19.20 and 22.11. In post 22.11, we saw that a microscope forms an intermediate image which is then magnified to give a final image. The picture above uses ray-tracing to show how the intermediate image, A’B’, is formed from the object AB. But I now want… Continue reading 22.12 Diffraction, Fourier transforms and image formation

Before you read this, I suggest that you read posts 22.1, 22.2 and 22.3. The picture shows a microscope. Light passes through a bi-convex lens called the condenser and then through a thin specimen that scatters the light. This scattered light then passes through another lens called the objective. The objective acts in the same… Continue reading 22.11 The microscope

Introduction We first met the mathematical operation of differentiation in post 17.4. But more information on this technique has appeared in many other posts. The purpose of this post is to bring all this information together in one place and to add some more to provide a single post on differentiation. In post 17.4, we… Continue reading 22.10 Differentiation

Before you read this, I suggest you read posts 17.15 and 17.16. About 40 years ago, Brian Pullan was Head of the Department of Medical Biophysics in the University of Manchester. Late last year, he sent me a problem to think about – it’s in the next paragraph. An ideal plane flies in a straight… Continue reading 22.9 More about flying

To understand this post you need to be familiar with the contents of post 18.2. The picture above shows cables supported by pylons; each section of cable hangs from two fixed points. Between these points, the force of gravity stretches the cable so that it falls into a curve. Until the early seventeenth century, people… Continue reading 22.8 The catenary

Before you read this, I suggest you read post 22.6. In post 22.6, we looked at the path taken by a ray when it is reflected by a concave surface. We looked at two types of concave surface. In the first, a section of the surface was the arc of a circle; in the second,… Continue reading 22.7 The caustic curve

Before you read this, I suggest you read post 22.4. When I wrote about reflection in post 22.4, I concentrated on reflection of light by a mirror. Concave mirrors are useful but the more familiar applications of reflection at concave surfaces involve focussing radio waves and microwaves from distant objects. Examples include radio-telescopes, receivers for… Continue reading 22.6 Reflection at concave surfaces – the satellite dish