Mirrors and Lenses

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Optics

• Mirrors and Lenses

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Regular vs. Diffuse Reflection

• Smooth, shiny surfaces have a regular reflection

Rough, dull surfaces have a diffuse
reflection. Diffuse reflection is when light is
scattered in different directions
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Reflection

• We describe the path of light as straight-line
  rays
• Reflection off a flat surface follows a simple
  rule
• angle in (incidence) equals angle out
  (reflection)
• angles measured from surface normal
  (perpendicular)

Laws of reflection
1 )The incident ray,
the reflected ray
and the normal
all lie in the same plane.
2)The incident angel the reflected angel
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24-1 mirrors
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An object viewed using a flat mirror appears to
be located behind the mirror, because to the
observer the diverging rays from the source
appear to come from behind the mirror
The image distance behind the mirror equals
the object distance from the mirror   The
image height h equals the object height h so
that the lateral magnification
  The image has an apparent left-right
reversal   The image is virtual, not real!

• 1- Virtual images - light rays do not meet and
  the image is always upright or right-side-up and
  also it cannot be projected Image only seems to
  be there
• Real images - always upside down and are formed
  when light rays actually meet

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example

• If the angle of incidence of a ray of light is
  42owhat is each of the following?
• A-The angle of reflection
  (42o)
• B-The angle the incident ray makes with the
  mirror (48o)
• C-The angle between the incident ray and the
  reflected
  (90o)

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Now you look into a mirror and see the image of
yourself.
a) In front of the mirror.
b) On the surface of the mirror.
C)Behind the mirror.
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Example
A girl can just see her feet at the bottom edge
of the mirror.
Her eyes are 10 cm below the top of her head.
(a) What is the distance between the girl and her
image in the mirror?
? Distance 150 ? 2 300 cm
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Signs Image size and magnification
images can be upright (positive image size h) or
inverted (negative image size h) Define
magnification m h/h Positive magnification
image orientation unchanged relative to
object Negative magnification image inverted
relative to object l m l lt 1 if image is smaller
than object l m l gt 1 if image is bigger than
object l m l 1 if image is same size as object
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24-2 Thin Lenses
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A lens is a transparent material made of glass or
plastic that refracts light rays and focuses (or
appear to focus) them at a point
A converging lens will bend incoming light that
is parallel to the principal axis toward the
principal axis.Any lens that is thicker at its
center than at its edges is a converging lens
with positive f. A diverging lens will bend
incoming light that is parallel to the principal
axis away from the principal axis.Any lens that
is thicker at its edges than at its center is a
diverging lens with negative f
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Rules For Converging Lenses

1. 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.
2. 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.
3. 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.

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Ray Diagram for Converging Lens, S gt f

• The image is real
• The image is inverted
• The image is on the back side of the lens

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S-
S
s
S-
S
S-
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Ray Diagram for Converging Lens, S lt f

• The image is virtual
• The image is upright
• The image is larger than the object
• The image is on the front side of the lens

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Object Outside 2F
Real inverted diminished
1. The image is inverted, i.e., opposite to the
object orientation.
2. The image is real, i.e., formed by actual
light on the opposite side of the lens.
3. The image is diminished in size, i.e., smaller
than the object.
Image is located between F and 2F
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Example 3. A magnifying glass consists of a
converging lens of focal length 25 cm. A bug is
8 mm long and placed 15 cm from the lens. What
are the nature, size, and location of image.
S 15 cm f 25 cm
S- -37.5 cm
The fact that S- is negative means that the image
is virtual (on same side as object).
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Object Between 2F and F
Real inverted enlarged
1. The image is inverted, i.e., opposite to the
object orientation.
2. The image is real formed by actual light rays
on opposite side
3. The image is enlarged in size, i.e., larger
than the object.
Image is located beyond 2F
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Object at Focal Length F
Parallel rays no image formed
When the object is located at the focal length,
the rays of light are parallel. The lines never
cross, and no image is formed.
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. Example Where must an object be placed to have
unit magnification (
M 1.00) (a) for a converging lens of focal
length 12.0 cm ? (b) for a diverging lens of
focal length 12.0 cm ?
b
a
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example A person uses a converging lens that
has a focal length of 12.5 cm to inspect a gem.
The lens forms a virtual image 30.0 cm away.
Determine the magnification. Is the image upright
or inverted?
solution
Since
, the image is upright.
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example A ray that starts from the top of an
object and runs parallel to the axis of the lens,
would then pass through the
a)principal focus of the lens
b)center of the lens
C)secondary focus of the lens
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Example 5 Derive an expression for calculating
the magnification of a lens when the object
distance and focal length are given.
From last equation -s M
Substituting for q in second equation gives . . .
Thus, . . .
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Diverging Thin Lens
Incoming parallel rays DIVERGE from a common
point FOCAL We still call this the point Same f
on both sides of lens Negative focal
length Thinner in center
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Ray Diagrams for Thin Lenses Diverging

• For a diverging lens, the following three rays
  are drawn
• Ray 1 is drawn parallel to the principal axis and
  emerges directed away from the focal point on the
  front side of the lens
• Ray 2 is drawn through the center of the lens and
  continues in a straight line
• Ray 3 is drawn in the direction toward the focal
  point on the back side of the lens and emerges
  from the lens parallel to the principal axis

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Ray Diagram for Diverging Lens

• The image is virtual
• The image is upright
• The image is smaller
• The image is on the front side of the lens

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Sign Conventions for Thin Lenses
Quantity Positive When Negative When
Object locatio (s) Object is in front of the lens Object is in back of the lens
Image location (s) Image is in back of the lens Image is in front of the lens
Image height (h) Image is upright Image is inverted
R1 and R2 Center of curvature is in back of the lens Center of curvature is in front of the lens
Focal length (f) Converging lens Diverging lens
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The power of lens
The reciprocal of the focal length the power
of lens
If the focal length f is measured in meters
then p measured in diopters if two lenses with
focal length f1 and f2 placed next to each other
are equivalent to a single lens with a focal
length f satisfying
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Spherical Aberration

• Results from the focal points of light rays far
  from the principle axis are different from the
  focal points of rays passing near the axis
• For a mirror, parabolic shapes can be used to
  correct for spherical aberration

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Spherical Aberration
With SA
SA free
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Chromatic Aberration

• Different wavelengths of light refracted by a
  lens focus at different points
• Violet rays are refracted more than red rays
• The focal length for red light is greater than
  the focal length
• for violet light
• Chromatic aberration can be minimized by the use
  of a combination of converging and diverging
  lenses

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Multiple lenses can be used to improve
aberrations
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Lens Aberrations
Chromatic aberration can be improved by combining
two or more lenses that tend to cancel each
others aberrations. This only works perfectly
for a single wavelength, however.
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An object is placed 6.0 cm in front of a convex
thin lens of focal length 4.0 cm. Where is the
image formed and what is its magnification and
power?
_
s
-
s
12 cm
s
M - 12 / 6 -2
Negative means real, inverted image
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Example 1. A glass meniscus lens (n 1.5) has a
concave surface of radius 40 cm and a convex
surface whose radius is 20 cm. What is the focal
length of the lens.
R1 20 cm, R2 -40 cm
f 80.0 cm
Converging () lens.
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Example What must be the radius of the curved
surface in a plano-convex lens in order that the
focal length be 25 cm?
R1 ?, f 25 cm
R2 0.5(25 cm)
R2 12.5 cm
Convex () surface.
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Example What is the magnification of a
diverging lens (f -20 cm) the object is located
35 cm from the center of the lens?
First we find q . . . then M
s 12.7 cm
M 0.364
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Example
An object is placed 20 cm in front of a
converging lens of focal length 10 cm. Where is
the image? Is it upright or inverted? Real or
virtual? What is the magnification of the image?
Real image, magnification -1
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Example
An object is placed 8 cm in front of a diverging
lens of focal length 4 cm. Where is the image?
Is it upright or inverted? Real or virtual? What
is the magnification of the image?
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Example
24(b). Given a lens with a focal length f 5 cm
and object distance p 10 cm, find the
following i and m. Is the image real or virtual?
Upright or inverted? Draw 3 rays.
Image is real, inverted.
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24(e). Given a lens with the properties (lengths
in cm) R1 30, R2 30, s 10, and n 1.5,
find the following f, s and m. Is the image real
or virtual? Upright or inverted? Draw 3 rays.
Real side
Virtual side
Image is virtual, upright.
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Example
An object is placed 5 cm in front of a converging
lens of focal length 10 cm. Where is the image?
Is it upright or inverted? Real or virtual? What
is the magnification of the image?
Virtual image, as viewed from the right, the
light appears to be coming from the (virtual)
image, and not the object. Magnification 2
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