<p class="MsoNormal"><span style="font-size: 1rem;">Optical lenses, such as the lenses in a camera
viewfinder, a telescope or a microscope, allow us to see the images of a wide
range of objects. In these instruments, a lens (or several lenses) takes the
image to the eye, which has a lens, too. But an image can be formed by many
lenses packed side by side in a layer. The eyes of insects have this
arrangement, with hundreds of small rod-shaped lenses, each directing part of the
image to the creature’s brain.</span></p><p class="MsoNormal"><div style="text-align: center;"><img src="https://upload.wikimedia.org/wikipedia/commons/1/10/Reflectionprojection.jpg" style="font-size: 1rem; width: 527.5px;"><a href="https://commons.wikimedia.org/wiki/File:Reflectionprojection.jpg" target="_blank"><sup>Real image of a lamp is projected onto a screen (inverted). Reflections of the lamp from both surfaces of the biconvex lens are visible.  Bcjordan, CC BY 2.0</sup></a></div><br></p><p class="MsoNormal"><span lang="">A photocopier has a similar imaging system. Up
to several million cylindrical ‘microlenses’, each only a few micrometres
across, form a flat array which scans the item being copied a line at a time.
The light from particular points on the copied item passes through the
microlenses, and on to the detector, to build up a complete image. The
refractive index of the microlenses is graded, which means the microlenses
don’t have to be ‘lens-shaped’.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Microlenses are also used in producing the
image on the liquid crystal display (LCD) screen of a portable laptop computer.
The brightness and clarity of the image are steadily being improved and, at the
same time, the energy required to power the equipment is being reduced.<o:p></o:p></span></p><h2><span lang="">The ideas in this chapter<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">In today’s world, images have become as
important as writing – or even speech – as a means of communicating ideas.
Images are rich in information: we say that ‘a picture says more than a
thousand words’. The figure below shows some symbols that clearly convey ideas
more rapidly and simply than words.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Every day we experience the communicating
power of images, particularly through television and advertising. Also, current
physics and technology convert complex data into images – from particle tracks
in accelerator detectors to ozone concentrations measured by satellites. In
this chapter, we will be looking at the basic science and the techniques used
to produce images.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">First, the chapter deals with the working of a
simple thin lens, and how lenses work in imaging devices such as the human eye,
cameras, telescopes and microscopes. Images are also produced by mirrors, both
flat and curved. The chapter goes on to show how images are displayed and
recorded. Finally, I will look briefly at some modern methods of imaging which
rely on advances in physics and involve complex technology.<o:p></o:p></span></p><h2><span lang="">HOW A CONVERGING LENS FORMS AN IMAGE<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">We are familiar with convex glass lenses. They
have equal surfaces that we think of as parts of a sphere, and are called
spherical (or simple) lenses. A lens which alters a plane wavefront to make the
light waves pass through a point, or focus, is called a converging or positive
lens. The wavelengths of the light are shorter after they pass across the
air-glass boundary. This is because the speed of the waves is less in glass
than in air, and the waves don’t go as far in each period of the wave motion.
This drop-in speed causes refraction, meaning that the light changes direction
wherever the wavefront is not parallel to the boundary.</span></p><p class="MsoNormal"><img src="https://upload.wikimedia.org/wikipedia/commons/c/c7/Lens_and_wavefronts.gif" style="width: 183px; float: left;" class="note-float-left"><div style="text-align: center;"><a href="https://commons.wikimedia.org/wiki/File:Lens_and_wavefronts.gif" target="_blank"><a href="https://commons.wikimedia.org/wiki/File:Lens_and_wavefronts.gif" target="_blank" style="background-color: rgb(255, 255, 255); font-size: 1rem;"><sup>Lenses can be used to focus light. Oleg Alexandrov, Public Domai</sup>n</a><br></a></div></p><p class="MsoNormal"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">Wave diagrams like above are hard to draw, and
they also hide some of the features of the light paths. Here, it makes sense to
revert to an old but very useful model of light which assumes that light
travels in straight lines. The figure shows just some of the light rays. The
rays show the direction of the waves, which means that the rays are at right
angles to the wavefront. When a ray hits the glass surface, it is refracted as
shown. Notice that the light ray hitting the centre of the lens does so at 90°
and that light rays increasingly far from the centre of the lens hit the
surface at smaller and smaller angles. I will return to this soon.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Look at the figure below, which shows light
passing through a plane surface, such as the surface of a glass block. The line
at right angles to the boundary is the normal, and we can see that the angle i
made with the normal by the incident ray is greater than the angle r of the
refracted ray. At the same time, as i increases, so r increases, while
remaining less than i. This shows that the light rays are obeying <b>Snell’s</b>
<b>law</b>, the <b>law of refraction</b>:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">sine of angle of
incidence/sine of angle of refraction = sin i/sin r = constant, n<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">The constant n is the refractive index (air to
glass for glass lenses). Looking at the <b>figure</b> in close-up, it shows
rays from a point source passing through a lens. The radius lines of the curved
surface are shown extended beyond the surface as normal lines. We can see again
that the law of refraction applies to the rays as they cross the air-glass boundary.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The spherical geometry of the simple lens
makes the rays converge (but not accurately) to one point or focus. For
parallel rays (that form a plane wavefront), is called the principal focus. The
distance of this point from the centre of the lens is called the focal length
of the lens. A lens has two principal focuses (or foci), one on each side of
the lens, at equal distances from it.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Refraction_at_interface.svg/535px-Refraction_at_interface.svg.png" style="width: 527.5px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Refraction_at_interface.svg" target="_blank"><sup>Refraction of a light ray. Ulflund , CC0</sup></a><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">In practice, the focus for simple spherical
lenses is only at a point if the diameter of the lens is very small compared
with the radius of curvature of its surfaces. Otherwise, the lens forms a
partly blurred image. A lens defect like this, caused either by the shape or
the material of the lens, is called an aberration. For a lens with spherical
geometry, it is called <b>spherical</b> <b>aberration</b>. Removing aberrations
is technically difficult, which explains why good optical instruments, such as
camera lenses, are expensive.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/92/Spherical_aberration_2.svg/474px-Spherical_aberration_2.svg.png" style="width: 474px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Spherical_aberration_2.svg" target="_blank"><sup>On top is a depiction of a perfect lens without spherical aberration: all incoming rays are focused in the focal point. The bottom example depicts a real lens with spherical surfaces, which produces spherical aberration. Mglg, Public Domain</sup></a><span lang=""><o:p><br></o:p></span></p><h2><span lang="">PREDICTING THE IMAGE<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">From a diagram showing how a simple lens forms
an image of an object, the position and size of an image either by drawing or
by using formulae can be predicted.<o:p></o:p></span></p><h3><span lang="">Drawing to find the image<o:p></o:p></span></h3><p class="MsoNormal"><span lang="">We can draw any number of rays to help us find
the position and size of an image, but the three rays that are most helpful to
draw are shown, with the usual labels we use when drawing ray diagrams. In an
upright object OX close to a lens. The object could be anything, but by
convention it is drawn simply as an arrow. Any ray that is parallel to the
principal axis of the lens is refracted to pass through the principal focus, F.
In this way, we can predict the direction of the ray. Note that in ray diagrams
such as this, the rays are assumed to change direction at a line that represents
a plane in the centre of the lens.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">We use the same idea for ray 2. Going through
F’, it emerges from the lens parallel to the principal axis. The third useful
line, for ray 3, goes straight through the centre of the lens – it does not
deviate. (But at the centre of the lens, the faces are parallel to each other.
If the lens is thin compared with the distances of object and image, which we
assume, the slight sideways displacement of the ray is not significant.)</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/Lens3.svg/542px-Lens3.svg.png" style="width: 527.5px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Lens3.svg" target="_blank"><sup>A camera lens forms a real image of a distant object. w:en:DrBob - w:en:File:Lens3.svg, GFDL</sup></a><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">All three rays pass through the same point, Y.
They all started at X, and it is clear that a screen placed at Y would catch
them all together again: Y is a focused line of X. Similarly, any point on OX
would give a focused image of itself somewhere between I and Y. IY is a real
image. A real image is one that can be caught on a screen: surprisingly some
images can’t and are called virtual images. These construction rays can be
drawn to scale to find the position and relative size of the image of any
object placed in front of the lens. Objects viewed through a lens, and their
images, are usually much smaller than the distances they are from the lens. In
such cases, it is best to make the vertical scale larger than the horizontal
one<o:p></o:p></span></p><h3><span lang="">Finding the image by formula<o:p></o:p></span></h3><p class="MsoNormal"><span lang="">It is usually quicker and more accurate to
find the position and size of an image by using the <b>lens</b> <b>formula</b>:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">1/u + 1/v = 1/f<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">Where u is the distance of the object from the
lens centre, i.e the object distance. v is the distance of the image from the
lens centre, the image distance, and f is the focal length of the lens. To find
the size of the image we can use the equation<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Image size = object
size </span><span lang="">×</span><span lang=""> V/U.<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">You can now find the position and size of any
image simply by inserting the other given values in the formula.<o:p></o:p></span></p><h2><span lang="">THE IMAGE IN A DIVERGING LENS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">The figure below shows a lens with concave
spherical surfaces and what happens to parallel light rays (that is, a plane
wavefront coming from a distant object) when they pass through it. The rays are
refracted so that they seem to diverge from a single point, F. This point is
the principal focus of a diverging lens. As light doesn’t actually come from
the point, or pass through it, it is a virtual focus. <o:p></o:p></span></p><p class="MsoNormal"><span lang="">The figure shows how a diverging lens forms an
image of an object. As for a converging lens, you would see the image by
looking at the object through the lens. But light doesn’t actually pass back
through the diverging lens to the image so you cannot catch the image on a
screen. It is, therefore, a virtual image.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Lens1b.svg/522px-Lens1b.svg.png" style="width: 522px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Lens1b.svg" target="_blank"><sup>Diverging lens. DrBob, CC BY-SA 3.0</sup></a><span lang=""><o:p><br></o:p></span></p><h3><span lang="">The sign convention<o:p></o:p></span></h3><p class="MsoNormal"><span lang="">The lens formula works for all simple optical
devices (even mirrors). But we have to know whether the images, principal
lenses – and even objects – are real or virtual. Where they are virtual, the convention
is to give negative values to distances measured from them to the lens or
mirror. For example, the principal focus of a diverging lens is virtual, so its
focal length is given a negative sign.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Suppose I place a real object 20 cm from the
diverging lens. The principal focus of the lens is 10 cm from the lens, so its
focal length is -10 cm. The lens formula gives:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">1/20 + 1/v = -1/10<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">So: 1/v = -1/10 – 1/20
= -3/20<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">And: v = -20/3 = - 6.7
cm<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">So the distance of the image from the lens
centre is 6.7 cm, and the negative sign tells us that the image is also
virtual.<o:p></o:p></span></p><h2><span lang="">THE POWER OF A LENS AND ITS IMAGE QUALITY<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">In optics, lenses are usually described in
terms of their power. The more powerful the lens, the closer to the lens is the
image that the lens forms of a distant object. The power of a lens is defined
as the reciprocal of its focal length f measured in metres:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Power = 1/f<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">The unit of power is called the <b>dioptre</b>,
symbol D, and so a lens of focal length +10 cm (0.1 m) has a power of +10 D. A
diverging lens of focal length -5 cm (-0.05 m) has a power of -20 D. This way
of describing lenses lets us work out what happens when two lenses are used
together. The combined power of the lenses is simply the sum of the powers of
each lens, bearing in mind their signs.<o:p></o:p></span></p><h2><span lang="">THE CAMERA LENS AS AN EXPENSIVE HOLE<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">We have seen that the quality of the image
made by a lens depends on its shape. Image quality also depends on the aperture
of the lens, that is, the part of the lens through which light is allowed to
pass. (Though the lens diameter is fixed, the aperture can be varied.)<o:p></o:p></span></p><p class="MsoNormal"><span lang="">A lens of large diameter captures more light
and produces a brighter image than a smaller diameter lens. However, it is
difficult and expensive to correct for aberrations in large aperture lenses.
So, for example, in ordinary cameras with a single lens, the lens is usually
‘stopped down’ to make the picture sharper. The light used to form the image
passes through the central region only of the lens, and this reduces spherical
aberration.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The quality of the image is also affected by
diffraction. The image is blurred as points on the object become circular
diffraction patterns. Points on the image subtending an angle smaller than a
certain value of </span><span lang="">θ</span><span lang=""> are not seen as
separate; their resolution is not possible. </span><span lang="">θ</span><span lang=""> is determined by wavelength </span><span lang="">λ</span><span lang=""> and aperture, d
in the <b>Rayleigh criterion</b>:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">θ = λ/d<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">Diffraction effects are reduced when the
aperture is large, so accurate optical instruments have a design conflict.
Large aperture means better resolution, as the Rayleigh criterion tells us, but
more spherical aberration. Small aperture reduces aberration but worsens
resolution.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">I will like to stop here for now. In my next
post, I will discuss on mirrors and some optical instruments with two
components.</span></p><p class="MsoNormal"><span lang=""><br></span><span style="font-size: 1.714rem; font-weight: bold;">REFERENCES</span></p><p><a href="https://www.ldoceonline.com/Physics-topic/imaging" target="_blank">https://www.ldoceonline.com/Physics-topic/imaging</a><br></p><p><a href="https://phy.duke.edu/research/research-areas/imaging-medical-physics" target="_blank">https://phy.duke.edu/research/research-areas/imaging-medical-physics</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://www.chegg.com/homework-help/questions-and-answers/245-converging-lens-forms-image-850mm-tall-real-object-image-115cm-left-lens-350cm-tall-er-q2745638" target="_blank">https://www.chegg.com/homework-help/questions-and-answers/245-converging-lens-forms-image-850mm-tall-real-object-image-115cm-left-lens-350cm-tall-er-q2745638</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://www.physicsclassroom.com/class/refrn/Lesson-5/Converging-Lenses-Ray-Diagrams" target="_blank">https://www.physicsclassroom.com/class/refrn/Lesson-5/Converging-Lenses-Ray-Diagrams</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://www.physicsclassroom.com/class/refrn/Lesson-5/Converging-Lenses-Object-Image-Relations#:~:text=A%20converging%20lens%20produced%20a,thus%20allowing%20for%20easier%20viewing." target="_blank">https://www.physicsclassroom.com/class/refrn/Lesson-5/Converging-Lenses-Object-Image-Relations#:~:text=A%20converging%20lens%20produced%20a,thus%20allowing%20for%20easier%20viewing.</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://www.britannica.com/technology/spherical-aberration" target="_blank">https://www.britannica.com/technology/spherical-aberration</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://en.wikipedia.org/wiki/Spherical_aberration" target="_blank">https://en.wikipedia.org/wiki/Spherical_aberration</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://www.effinghamschools.com/cms/lib4/ga01000314/centricity/domain/702/599-603.pdf" target="_blank">https://www.effinghamschools.com/cms/lib4/ga01000314/centricity/domain/702/599-603.pdf</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://www.azooptics.com/Article.aspx?ArticleID=675" target="_blank">https://www.azooptics.com/Article.aspx?ArticleID=675</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://courses.lumenlearning.com/physics/chapter/25-6-image-formation-by-lenses/" target="_blank">https://courses.lumenlearning.com/physics/chapter/25-6-image-formation-by-lenses/</a><span lang=""><o:p><br></o:p></span></p><p><a href="https://www.physicsclassroom.com/class/refrn/Lesson-5/Diverging-Lenses-Object-Image-Relations">https://www.physicsclassroom.com/class/refrn/Lesson-5/Diverging-Lenses-Object-Image-Relations</a><a href="https://www.physicsclassroom.com/class/refrn/Lesson-5/Diverging-Lenses-Object-Image-Relations" target="_blank"></a></p><p><a href="https://www.olympus-lifescience.com/en/microscope-resource/primer/java/lenses/diverginglenses/#:~:text=Negative%20lenses%20diverge%20parallel%20incident,center%20than%20at%20the%20edges." target="_blank">https://www.olympus-lifescience.com/en/microscope-resource/primer/java/lenses/diverginglenses/#:~:text=Negative%20lenses%20diverge%20parallel%20incident,center%20than%20at%20the%20edges.</a><br></p><p><a href="https://www.explainthatstuff.com/lenses.html" target="_blank">https://www.explainthatstuff.com/lenses.html</a><br></p><p><a href="https://www.photoreview.com.au/tips/lens-tips/lens-quality-and-image-sharpness/" target="_blank">https://www.photoreview.com.au/tips/lens-tips/lens-quality-and-image-sharpness/</a><br></p><p><a href="https://www.quora.com/How-do-different-lenses-affect-the-photo-quality">https://www.quora.com/How-do-different-lenses-affect-the-photo-quality</a><a href="https://www.quora.com/How-do-different-lenses-affect-the-photo-quality" target="_blank"></a></p><p><a href="https://en.wikipedia.org/wiki/Lens" style="background-color: rgb(255, 255, 255); font-size: 1rem;">https://en.wikipedia.org/wiki/Lens</a></p><p><a href="https://en.wikipedia.org/wiki/Lens" target="_blank"></a></p><p><br><a href="https://medium.com/photography-secrets/lenses-e033d2f77548" target="_blank">https://medium.com/photography-secrets/lenses-e033d2f77548</a><br><span lang=""><o:p><br></o:p></span></p>