Refraction
Refraction occurs as light passes across the boundary between two medium. Refraction is the
bending of the path of a light wave as it passes from one material to another material, and it is
caused by changing in speed experienced by a wave when it changes medium. A one-word
synonym for refraction is "bending."
As light travels from one medium to another, it changes speed, angle, and wavelength.
FST = Fast to Slow, Towards Normal
If a ray of light passes across the boundary from a material in which it travels Fast into a material
in which travels Slower, then the light ray will bend Towards the normal line.
SFA = Slow to Fast, Away From Normal
If a ray of light passes across the boundary from a material in which it travels Slow into a
material in which travels Faster, then the light ray will bend Away from the normal line.
Snell’s Law
When a light ray is transmitted into a new medium, the relationship between the angle of
incidence and the angle of refraction is given by the following equation:
ni * sin ( ) = nr * sin ( )
nmaterial =
index of refraction of the material
= angle of incidence
= angle of refraction
ni = index of refraction of the incident medium
nr = index of refraction of the refractive medium
As light travels from one medium to another, its speed, angle, and wavelength change. There
is also a relationship between the change in speed and change in wavelength which can be
defined as following equations:
n1*v1=n2*v2
n1*λ1=n2*λ2
It is convenient to define Index of Refraction n of a medium to be the ratio:
n=
speed of light in Vacuum c
=
speed of light in Medium v
c=3*108
The Critical Angle
The critical angle only takes place when both of the following two conditions are met:
A light ray is in the denser medium and approaching the less dense medium.
The angle of incidence for the light ray is greater than the so-called critical angle.
The critical angle is defined as the angle of incidence which provides an angle of refraction of
90-degrees. Make particular note that the critical angle is an angle of incidence value.
ni * sin ( ) = nr * sin ( )
ni * sin (
) = nr * sin (90 degrees)
ni * sin (
sin (
) = nr
) = nr/ni
= sin-1 (nr/ni)
Lenses
There are a variety of types of lenses. Lenses differ from one another in terms of their shape
and the materials from which they are made. We will categorize lenses as converging lenses and
diverging lenses.
Converging lens is a lens which converge rays of light which are traveling parallel to its
principal axis. Converging lenses can be identified by their shape; they are thicker across their
middle and thinner at their upper and lower edges.
Diverging lens is a lens which diverge rays of light which are traveling parallel to its principal
axis. Diverging lenses can also be identified by their shape; they are thinner across their middle
and thicker at their upper and lower edges.
As we begin to discuss the refraction of light rays and the formation of images by these two
types of lenses, we will need to use a variety of terms.
Principal axis: If a symmetrical lens is thought of as being a slice of a sphere, then there would
be a line passing through the center of the sphere and attaching to the mirror in the exact center
of the lens.
Vertical axis: A lens also has an imaginary vertical axis which bisects the symmetrical lens in
two.
Focal point: light rays incident towards either face of the lens and traveling parallel to the
principal axis will either converge or diverge. If the light rays converge (as in a converging lens),
then they will converge to a point. This point is known as the focal point of the converging lens.
If the light rays diverge (as in a diverging lens), then the diverging rays can be traced backwards
until they intersect at a point. This point is known as the focal point of a diverging lens. The
focal point is denoted by the letter F on the diagrams below. Note that each lens has two focal
points - one on each side of the lens. Every lens has two possible focal points.
Focal length: The distance from the lens to the focal point is known as the focal length
(abbreviated by "f").
2F point: This is the point on the principal axis which is twice as far from the vertical axis as
the focal point is.
Refraction Rules for a Converging Lens
Any incident ray traveling parallel to the principal axis of a converging lens will refract through
the lens and travel through the focal point on the opposite side of the lens.
Any incident ray traveling through the focal point on the way to the lens will refract through the
lens and travel parallel to the principal axis.
An incident ray which passes through the center of the lens will in effect continue in the same
direction that it had when it entered the lens.
Refraction Rules for a Diverging Lens
Any incident ray traveling parallel to the principal axis of a diverging lens will refract through
the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass
through the focal point).
Any incident ray traveling towards the focal point on the way to the lens will refract through
the lens and travel parallel to the principal axis.
An incident ray which passes through the center of the lens will in effect continue in the same
direction that it had when it entered the lens.
.
Image Characteristics for Converging Lens
The best means of summarizing this relationship is to divide the possible object locations into
five general areas or points:
Case 1: the object is located beyond 2F
Case 2: the object is located at 2F
Case 3: the object is located between the F and 2F
Case 4: the object is located at the focal point (F)
Case 5: the object is located in front of the focal point (F)
Case 1: the object is located beyond 2F
When the object is located beyond 2F:
• The image will be between the F and 2F in opposite
side of the lens.
• The image will be an inverted.
• The image is reduced in size; the magnification is less than 1.
• The image is real.
Case 2: the object is located at 2F
When the object is located at 2F:
• The image will also be located at 2F in opposite side of the lens.
• The image will be inverted
• The image dimensions are equal to the object dimensions.
• The image is real
Case 3: the object is located between the F and 2F
When the object is located between F and 2F:
•
•
•
•
The image will be beyond 2F in opposite side of the lens.
The image will be inverted
The image dimensions are larger than the object dimensions.
The image is real.
Case 4: the object is located at the focal point (F)
When the object is located at the focal point:
• No image is formed (or the image will be at infinity).
• The reflected rays neither converge nor diverge. After reflecting, the light rays are
traveling parallel to each other and cannot produce an image.
•
If we assume that an image is formed at infinity then:
o The image will be inverted.
o The image dimensions are larger than the object dimensions. The magnification
is greater than 1.
o The image is a real image.
Case 5: the object is located in front of the focal point (F)
When the object is located in front of F:
• The image will be on the same side of the lens.
• The image will be an upright image.
• The image is enlarged.
• The image is virtual.
Summary of Different forms of image in
Converging Lens
Eight different object locations are drawn and labeled with a number; the corresponding image
locations are drawn in blue and labeled with the identical number.
Concave mirrors can produce both real and virtual images.
The Converging Lens Equation
The lens equation expresses the quantitative relationship between the object distance (p), the
image distance (q), and the focal length (f). The equation is stated as follows:
1 1 1
= +
f
p q
The Magnification equation relates the ratio of the image distance and object distance to the
ratio of the image height (h’) and object height (h). The magnification equation is stated as
follows:
M=-
q h'
=
p h
These two equations can be combined to yield information about the image distance and image
height if the object distance, object height, and focal length are known.
The focal length is related to the curvature of its front, back surfaces, and the index of refraction
(n) of the lens material by:
1
1
1
= (n − 1)( − )
f
R1 R2
Image Characteristics for Diverging Lens
Unlike converging lenses, diverging lenses always produce images which share same
characteristics. The location of the object does not effect the characteristics of the image. As
such, the characteristics of the images formed by diverging lenses are easily predictable.
The diagrams above shows that in each case, the image is:
1. Located behind the lens
2. A virtual image
3. An upright image
4. Reduced in size (i.e., smaller than the object)
Summary of Different forms of image in
Diverging Lens
The diagram below shows five different object locations (drawn and labeled in red) and their
corresponding image locations (drawn and labeled in blue).
The Diverging Lens Equation
The lens equation expresses the quantitative relationship between the object distance (p), the
image distance (q), and the focal length (f). The equation is stated as follows:
1 1 1
= +
f
p q
The Magnification equation relates the ratio of the image distance and object distance to the
ratio of the image height (h’) and object height (h). The magnification equation is stated as
follows:
M=-
q h'
=
p h
These two equations can be combined to yield information about the image distance and image
height if the object distance, object height, and focal length are known.
The focal length is related to the curvature of its front, back surfaces, and the index of
refraction (n) of the lens material by:
1
1
1
= (n − 1)( − )
f
R1 R2
Problem Solving
Front
Back
p positive
q negative
p negative
q positive
Incident light
Reflected light
f is always positive for converging lens.
f is always negative for diverging lens.
R1 and R2 are positive when the center of curvature is in back of lens.
R1 and R2 are negative when the center of curvature is in front of lens.
p
+
+
q
+
-
M
+
q h'
=
p h
When M is positive, the image will be virtual, upright, and in front of the lens. M is positive
because q is negative in this situation.
When M is negative, the image will be real, inverted, and in back of the lens. M is negative
because q is positive in this situation.
M=-
p 〉 q or h 〉 h'
M 〈1
p 〈 q or h 〈 h'
M 〉1
p = q or h=h’
M =1
EYE
Diopter
The power of a lens is measured by opticians in a unit known as a diopter. A diopter is equal to
the reciprocal of the focal length.
Diopter =
Farsightedness
1
(focal length needs to be in meter)
focal length
Farsightedness is the inability of the eye to focus on nearby objects. The farsighted eye has no
difficulty viewing distant objects. The farsighted eye is assisted by the use of a converging lens.
Nearsightedness
Nearsightedness is the inability of the eye to focus on distant objects. The nearsighted eye has
no difficulty viewing nearby objects. The cure for the nearsighted eye is to equip it with a
diverging lens.