Chapter 23:Mirrors and Lenses

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Chapter 23Mirrors and Lenses

• Flat Mirrors

Homework assignment 20,24,42,45,51

• Image of a point source

The reflected rays entering eyes look as though
they had come from image P.
P
virtual image
P
Light rays radiate from a point object at P in
all directions.
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• Image of a point source on a flat mirror (contd)

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Flat Mirrors

• Image formation on a flat mirror

s (s) is the image (object) distance
s s

• Sign Rules
• Sign rule for the object distance
• When object is on the same side of the
  reflecting
• or refracting surface as the incoming
  light, the object
• distance s is positive. Otherwise it is
  negative.
• (2) Sign rule for the image distance
• When image is on the same side of the reflecting
  or
• refracting surface as the outgoing light,
  the image
• distance s is positive. Otherwise it is
  negative.
• (3) Sign rule for the radius of curvature of a
  spherical
• surface
• When the center of curvature C is on the same
  side
• as the outgoing light, the radius of the
  curvature is
• positive. Otherwise it is negative.

s
4
Flat Mirrors

• Image of an extended object on a flat mirror

Multiple image due to multiple Reflection by two
mirrors
image is erect image is virtual
h
h
S1
S2
S3
m h/h1 lateral magnification
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Flat Mirrors

• Rotation of mirror

When a flat mirror is rotated, how Much is the
image rotated?
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Flat Mirrors

• Example

What is the size of the smallest vertical plane
mirror in which a woman of height h can see her
full-length?
Solution
x
x/2
The minimum length of mirror for a woman to see
her full height h Is h/2 as shown in the figure
right.
(h-x)/2
h-x
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• Image Formed by Spherical Mirrors

• Concave and convex mirrors

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• Image Formed by Spherical Mirrors

• Focal points at concave and convex mirror

Focal point or focus Point F at which rays from
a source point are
brought together (focused) to form an
image. Focal length Distance f from mirror where
focus occurs. fR/2 where
R is the radius of a spherical mirror.
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• Image Formed by Spherical Mirrors

• Focal points at a concave mirror

h
object
d
image
s
If
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• Image Formed by Spherical Mirrors

• Image of an extended object at a concave mirror

real image
Principle rays Light rays that can be traced
(more easily) from the source
to the image 1. Parallel to
optical axis 2. Passing through the
focal point 3. Passing
through the center of curvature 4.
Passing through the center of the mirror surface
or lens
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• Image Formed by Spherical Mirrors

• Magnification of image at a concave mirror

h
h
When s,s gt0 , mlt0 inverted s/slt0,
mgt0 upright or
erect
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• Image Formed by Spherical Mirrors

• Example with a concave mirror

real image
real image
real image
virtual image
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• Image Formed by Spherical Mirrors

• Example with a concave mirror

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Image Formed by Spherical Mirrors

• Image at a convex mirror

s
s
f
f
R
s positive s negative (virtual image) R
negative f negative
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Image Formed by Spherical Mirrors

• Magnification of image at a convex mirror

For a convex mirror f lt 0
s
m gt 1 magnified m lt 1 minimized m gt 0 image
upright m lt 0 image inverted
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• Refraction at a spherical surface

• Refraction at a convex spherical surface

q1
q1-q2
For small angles
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• Refraction at a spherical surface

• Refraction at a concave spherical surface

For a concave surface, we can use the same formula
But in this case R lt 0 and f lt 0. Therefore the
image is virtual.
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• Refraction at a spherical surface

• Relation between source and image distance
• at a convex spherical surface

s
Snells law
For a convex (concave) surface, R gt(lt) 0.
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• Refraction at a spherical surface

• Example of a convex surface

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• Refraction at a spherical surface

• Example of a concave surface

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• Refraction at a spherical surface

• Example of a concave surface

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• Refraction at a spherical surface

• Example of a concave surface

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• Convex Lens

• Sign rules for convex and concave lens

• Sign Rules
• Sign rule for the object distance
• When object is on the same side of the
  reflecting
• or refracting surface as the incoming
  light, the object
• distance s is positive. Otherwise it is
  negative.
• (2) Sign rule for the image distance
• When image is on the same side of the reflecting
  or
• refracting surface as the outgoing light,
  the image
• distance i is positive (real image).
  Otherwise it is negative
• (virtual image).
• (3) Sign rule for the radius of curvature of a
  spherical
• surface
• When the center of curvature C is on the same
  side
• as the outgoing light, the radius of the
  curvature is
• positive. Otherwise it is negative.

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• Convex Lens

• Lens-makers (thin lens) formula

surface 2
surface 1
s
Image due to surface 1
s1 becomes source s2 for surface 2
R1gt0
R2lt0
s1 s and s2 s
Parallel rays (sinf.) w.r.t. the axis
converge at the focal pioint
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• Convex Lens

• Magnification

s
same as for mirrors
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• Convex Lens

• Object between the focal point and lens

A virtual image
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• Convex Lens

• Object position, image position, and
  magnification

real inverted image m lt 1
real inverted image m gt1
virtual erect image m gt1
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• Lens

• Types of lens

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• Lens

• Two lens systems

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• Lens

• Two lens systems (contd)

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• Lens

• Two lens systems (contd)

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• Lens

• Two lens systems (contd)

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• Aberration

sphere
paraboloid
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• Chromatic aberration

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• Gravitational lens

36

• Exercises

Problem (focal length of a zoom lens)
f2-f2
f1
ray bundle
f1
r0
I
Q
r0
r0
d
x
s2
d (variable)lt
s2
f1
f
Find the effective focal length f of the
combination lens.
Solution
(a)
(b)
(c)