1. Optics (Lecture 2)
Book Chapter 34,35

2. images
• An image is a reproduction of an object via light.
• If the image can form on a surface, it is a real
image. Examples of real images include the image seen on
a cinema screen. Real images can be produced by concave
mirrors and converging lenses.
• It can exist even if no observer is present. If the
image requires the visual system of an observer,
it is a virtual image. A simple example is a flat mirror
• A real image occurs where rays converge, whereas a
virtual image occurs where rays only appear to
converge.

3. Flat Mirror
an object placed in front of a flat mirror.

5. Ray diagram of Mirror

6. Sign convention

7. Concave Mirror
When the object is located so that the center of curvature lies
between the object and a concave mirror surface, the image is real,
inverted, and reduced in size.

8. Concave Mirror
When the object is located between the focal point and a concave
mirror surface, the image is virtual, upright, and enlarged.

9. When the object is in front of a convex mirror, the image is
virtual, upright, and reduced in size

10. Spherical Mirror Equation
• The equation for image formation by rays
near the optic axis (paraxial rays) of a
mirror has the same form as the thin lens
equation:
• From the geometry of the spherical mirror,
note that the focal length is half the radius
of curvature:
1 1 1
O f i
 
1
f
r
 

11. • As in the case of lenses, the cartesian sign
convention is used here, and that is the
origin of the negative sign above. The
radius r for a concave mirror is a negative
quantity (going left from the surface), and
this gives a positive focal length, implying
convergence.

12. Exercise
The M <1; the image is smaller than the object, and the –ve sign for M tells us that the
image is inverted. Because q is positive, the image is located on the front side of the
mirror and is real.
The object is positioned at the focal point
of a mirror are reflected so that the image
is formed at an infinite distance from the
mirror;

13. The image is twice as large as the object, and the positive
sign for M indicates that the image is upright

14. Six possible ways in which an image
can be formed by refraction through a
spherical surface of radius r and
center of curvature C. The surface
separates a medium with index of
refraction n1 from a medium with
index of refraction n2.
The point object O is always in the
medium with n1 to the left of the
surface. The material with the lesser
index of refraction is unshaded
Real images are formed in (a) and
(b); virtual images are formed in the
other four situations.
Solve Example 34.2

16. Ray diagram of Lens
• The image formed by a single lens can be located and
sized with three principal rays. Examples are given for
converging and diverging lenses and for the cases
where the object is inside and outside the principal focal
length.
• The "three principal rays" which are used for visualizing
the image location and size are:
– A ray from the top of the object proceeding parallel to the
centerline perpendicular to the lens. Beyond the lens, it will pass
through the principal focal point. For a negative lens, it will
proceed from the lens as if it emanated from the focal point on
the near side of the lens.

17. – A ray through the center of the lens, which will be un-deflected.
– A ray through the principal focal point on the near side of the
lens. It will proceed parallel to the centerline upon exit from the
lens. The third ray is not really needed, since the first two locate
the image.

18. Thin Lens
• A lens is a transparent object with two refracting
surfaces whose central axes coincide. The
common central axis is the central axis of the
lens. When a lens is surrounded by air, light
refracts from the air into the lens, crosses
through the lens, and then refracts back into the
air.
• Each refraction can change the directionof travel
of the light.

20. Example
The negative sign tells us that the image is in front of the lens
and virtual,

21. Example
The positive sign indicates that the image
is in back of the lens and real.
the image is inverted.

23. The image is enlarged, and the
positive sign for M tells us that the image is upright,

24. Example

26. Thin Lens

28. (a) A real, inverted image I is formed by a
converging lens when the object O is outside the
focal point (b) The image I is virtual and has the
same orientation as O
when O is inside the focal point.
(c) A diverging lens forms a virtual image I, with
the same orientation as the object O, whether O
is inside or outside the focal point of the lens.

29. Ray Diagrams for Convex Lenses
• For an object outside
the focal point, a
real inverted image will
be formed.
• For an object inside the
focal point, a virtual
erect image will be
formed.

30. Real Image Formation
• If a luminous object is placed at a distance greater than
the focal length away from a convex lens, then it will
form an inverted real image on the opposite side of the
lens. The image position may be found from the lens
equation or by using a ray diagram.

31. Virtual Image Formation
• Diverging lenses form reduced, erect, virtual images.
Using the common form of the lens equation, f, P and i
are negative quantities.

32. Ray Diagrams for Concave Lenses
• The ray diagrams for concave lenses inside and outside
the focal point give similar results: an erect virtual
image smaller than the object. The image is always
formed inside the focal length of the lens.

33. Focal Length and Lens Strength
• The most important characteristic of a lens is
its principal focal length, or its inverse which is
called the lens strength or lens "power".
• Optometrists usually prescribe corrective
lenses in terms of the lens power in diopters.
• The lens power is the inverse of the focal length
in meters: the physical unit for lens power is
1/meter which is called diopter.

35. Lens-Maker's Formula
• For a thin lens, the power is approximately
the sum of the surface powers.
• The radii of curvature here are measured according to the Cartesian
sign convention.
• For a double convex lens the radius R1 is positive since it is
measured from the front surface and extends right to the center of
curvature. The radius R2 is negative since it extends left from the
second surface
0
0 1 2
1 1
lens
lens
n n
P
n R R
 

 
 
 

36. lmage Formation
• Spherical mirrors, spherical refracting surfaces, and thin
lenses can form images of a source of light the object-by
redirecting rays emerging from the source.
• The image occurs where the redirected rays cross
(forming a real image) or where backward extensions of
those rays cross (forming a virtual image).
• If the rays are sufficiently close to the central axis
through the spherical mirror, refracting surface, or thin
lens, we have the following relations between the object
distance o or p (which is positive) and the image
distance i (which is positive for real images and negative
for virtual images)

38. Convex Mirror Image
• A convex mirror forms a virtual image.

39. • Using a ray parallel to the principal axis
and one incident upon the center of the
mirror, the position of the image can be
constructed by back-projecting the rays
which reflect from the mirror.
• The virtual image that is formed will
appear smaller and closer to the mirror
than the object.

40. Concave Mirror Image
• If the object is outside the focal length, a
concave mirror will form a real, inverted image.

41. Concave Mirror Image
If an object is placed inside the focal length of a
concave mirror, and enlarged virtual and erect image
will be formed behind the mirror

43. Huygen’s Principle

49. Diffraction
• When waves encounter an edge, an obstacle, or an
aperture the size of which is comparable to the
wavelength of the waves, those waves spread out as
they travel and, as a result, undergo interference. This is
called diffraction
• Diffraction is the constructive and destructive
interference of two beams of light that results in a wave-
like pattern.

50. Diffraction
• If a wave encounters a barrier that has an opening of
dimensions similar to the wavelength, the part of the
wave that passes through the opening will flare (spread)
out-will diffract-into the region beyond the barrier.

62. Locating the Fringes

68. Coherence
Two sources of light are said to be coherent if the waves
emitted from them have the same frequency and are
'phase-linked'; that is, they have a zero or constant phase
difference

74. Newton’s Ring
• Newton’s Ring is an interference pattern caused
by the reflection of light between two surfaces -
a spherical surface and an adjacent flat surface.
passing through, and λ is the wavelength of the
light passing through the glass.
• When viewed with monochromatic light it
appears as a series of concentric, alternating
bright and dark rings centered at the point of
contact between the two surfaces.

75. • The light rings are caused by constructive
interference between the light rays
reflected from both surfaces, while the
dark rings are caused by destructive
interference.
• Also, the outer rings are spaced more
closely than the inner ones.

76. • The radius of the Nth Newton's bright ring
is given by
• where N is the bright ring number, R is the
radius of curvature of the lens the light is
1/2
1
2
N
r N R

 
 
 
 
 
 
 

77. Fraunhofer diffraction
• Fraunhofer diffraction is the special case where
the incoming light (monochromatic) is assumed
to be parallel and the image plane is assumed to
be at a very large distance compared to the
diffracting object.
• It occurs when planar waves are passed through
an aperture or slit causing only the size of an
observed aperture image to change due to the
far-field location of observation and the
increasingly planar nature of outgoing diffracted
waves passing through the aperture.

78. Fresnel diffraction
• Fresnel diffraction refers to the general case.
• Fresnel diffraction or near-field diffraction is a process
of diffraction that occurs when a wave passes through an
aperture and diffracts in the near field, causing
any diffraction pattern observed to differ in size and
shape, depending on the distance between the aperture
and the projection.

79. • An example of an optical setup that displays Fresnel diffraction
occurring in the near-field. On this diagram, a wave is diffracted and
observed at point σ. As this point is moved further back, beyond the
Fresnel threshold or in the far-field, Fraunhofer diffraction occurs.

80. Summary
• Fresnel diffraction occurs when:
• Fraunhofer diffraction occurs when:
• a - aperture or slit size,
• λ - wavelength,
• L - distance from the aperture
2
1
a
F
L
 
2
1
a
F
L
