Geometrical Optics-Classical Physics-Handouts, Lecture notes of Classical Physics

This course includes alternating current, collisions, electric potential energy, electromagnetic induction and waves, momentum, electrostatics, gravity, kinematic, light, oscillation and wave motion. Physics of fluids, sun, materials, sound, thermal, atom are also included. This lecture includes: Geometrical, Optics, Waves, Light, Reflected, Object, Image, Incident, Ray, Normal, Direction, Surface, COncave, Convex

Typology: Lecture notes

2011/2012

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PHYSICS –PHY101 VU
© Copyright Virtual University of Pakistan
110
Sun
Moon Earth
SUN
Summary of Lecture 35 – GEOMETRICAL OPTICS
1. In the previous lecture we learned that light is waves,
and that waves spread out from every point. But in
many circumstances we can ignore the spreading
(diffraction and interference), and light can then be
assumed to travel along straight lines as rays. This
is hown by the existence of sharp shadows, as for
case of the eclipse illustrated here.
2. When light falls on a flat surface, the angle of
incidence equals the angle of reflection. You
can verify this by using a torch and a mirror,
or just by sticking pins on a piece of paper in
front of a mirror. But what if the surface is not
perfectly flat? In that case, as shown in fig. (b),
the angle of incidence and reflection are equal
at every point, but the normal direction differs
from point to point. This is called "diffuse
reflection". Polishing a surface reduces the
diffusiveness.
3. If you look at an object in the mirror, you
will see its image. It is not the real thing, and
that is why it is called a "virtual" image. You
can see how the virtual image of a candle is
formed in this diagram. At each point on the
surface, there is an incident and reflected ray.
If we extend each reflected ray backwards,
it appears as if they are all coming from the
same point. This point is the image of the tip
of the flame. If we take other points on the
candle, we will get their images in just the
same way. This way we will have the image
of the whole candle. The candle and its
image are at equal distance from the mirror.
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Sun

Moon

Earth SUN

Summary of Lecture 35 – GEOMETRICAL OPTICS

  1. In the previous lecture we learned that light is waves, and that waves spread out from every point. But in many circumstances we can ignore the spreading (diffraction and interference), and light can then be assumed to travel along straight lines as rays. This is hown by the existence of sharp shadows, as for case of the eclipse illustrated here.
  2. When light falls on a flat surface, the angle of incidence equals the angle of reflection. You can verify this by using a torch and a mirror, or just by sticking pins on a piece of paper in front of a mirror. But what if the surface is not perfectly flat? In that case, as shown in fig. (b), the angle of incidence and reflection are equal at every point, but the normal direction differs from point to point. This is called "diffuse reflection". Polishing a surface reduces the diffusiveness.
  3. If you look at an object in the mirror, you will see its image. It is not the real thing, and that is why it is called a "virtual" image. You can see how the virtual image of a candle is formed in this diagram. At each point on the surface, there is an incident and reflected ray. If we extend each reflected ray backwards, it appears as if they are all coming from the same point. This point is the image of the tip of the flame. If we take other points on the candle, we will get their images in just the same way. This way we will have the image of the whole candle. The candle and its image are at equal distance from the mirror.
  1. Here is another example of image formation. A source of light is placed in front of a bi-convex lens which bends the light as shown. The eye receives rays of light which seem to originate from a positon that is further away than the actual source.

Now just to make the point even more forcefully, in all three situations below, the virtual image is in the same position although the actual object is in 3 different places.

  1. Imagine that you have a sphere of radius R and that you can cut out any piece you want. The outside or inside surface can be silvered, as you want. You can make spherical mirrors in this way. These can be of two kinds. In the first case, the silvering can be on the inside surface of the sphere, in which case this is is called a convex spherical mirror. The normal directed from the shiny surface to the centre of the sphere (from which it was cut out from) is called the principal axis, and the radius of curvature is. The other situation is that in which the ou

R

tside surface is shiny. Again, the principal axis the same, but now the radius of curvature (by definition) is -. What does a negative curvature mean? It means precisely what has been illus

R

trated - a convex surface has a positive and a concave surface has a negative curvature.

f

Focusing light with lens Convergent lens

f

f

R 2 < 0^1 f^ =^ (^ nl −^1 )^ ⎛⎜⎝^ R^11 (^) − R^12 ⎞⎟⎠

R 1 > 0

  1. A lens is a piece of glass curved in a definite way. Because the refractive index of glass is bigger than one, every ray bends towards the normal. Here you see a double convex lens that focuses a beam of parallel rays. For a perfect lens, all the rays will converge to one single point that is (again) called the focus. The distance f is called the focal length. Of course, light can equally travel the other way, so if a point source is placed at the focus of a convex lens then a parallel beam of light will emerge from the other side. This is how some film projectors produce a parallel beam.

A concave lens does not cause a parallel beam to converge. On the contrary, it makes it diverge, as shown. Note, however, that if the rays are continued backwards, then they appear to come from one single point, which is here the virtual focus. The distance f is the focal length.

  1. Here is how a concave (or divergent) lens forms an image. An observer on the side opposite to the object will see the image upright and smaller in size than the object.

Divergent lens Object

Virtual and upright image

1 2 2

  1. A lens can be imagined as cut out of two spheres of glass as shown, with the spheres having radii R and R. Note that they tend to bend light in opposite ways. By convention, R is

1 2

negative. It is possible to show that the focal length of the

lens is , 1 n 1 1 1. f R R

= − ⎛^ − ⎞

  1. The following figure summarizes the shape of some common types of lenses.

Note that a flat surface has infinite radius of curvature. The focal legth of each can be calculated using the previous formula.

  1. The "strength" of a lens is measured in diopters. If the focal length of a lens is expressed in metres, the diopter of the lens is defined as 1/. If the refractive index of the glass in a lens is , then the diopters due to the first interf

D f n

1 2 1 1 2 2 1 2

ace and the second interface are, ( 1) / and (1 ) /. The total diopter of the lens is.

  1. For any optical system - meaning a collection of lenses and mirrors - we can def

D

D D = nR D = − n R D = D + D

ine a magnification factor as a ratio of sizes -- see the diagram below.

  1. The perfect lens will focus a parallel beam of rays all to exactly the same focus. But no lens is perfect, and every lens suffers from aberration although this can be made quite small by following one lens with another. Below you see an example of "spherical aberration". Rays crossing different parts of the lens do not reach exactly the same focus. This distorts the image. Computers can design lens surfaces to minimize this aberration.

Planar convex R 1 > 0 R 2 = infinity

Bi-concaveR R^1 < 0 2 > 0

Planar-concave R 1 = infinity R 2 > 0

CONVEX LENS CONCAVE LENS Bi-convex R 1 > 0 R 2 < 0

Ob Objjeecctt

OpOpttiiccaall EElleemmeenntt ImImaaggee hh hh′′

La Latteerraall MMaaggnniiffiiccaattiioonn MM == hh′′//hh

Spherical Aberration

Principal