Optics Course
(Phys 311)
Geometrical Optics
Reflection through Mirrors
Lecturer:
Dr Zeina Hashim
Phys
311
Geometrical Optics: Reflection (Mirrors)
Objectives covered in this lesson :
1. Images: real and virtual.
2. Mirrors: planar, spherical, aspherical.
3. Mirrors: convex and concave
4. Reflection through mirrors.
5. Object distance, image distance, and focal length.
6. Lateral magnification.
Lesson 1 of 1
Slide 1
Phys
311
Geometrical Optics: Reflection (Mirrors)
Lesson 1 of 1
Slide 2
1 Images :
An image: is a reproduction of an object via light. Images form from redirected rays
of an object through mirrors and refracting surfaces (e.g. lenses).
They are images which require the visual system of an observer.
Virtual
Images
Real
Images
They form on the opposite side of a mirror of where the object is.
They form when the backward extensions of the object’s redirected rays cross.
They are images which can form on a surface & can exist even if no observer is present.
They form on the side of a mirror where the object is.
They form when the redirected rays cross.
Phys
311
Geometrical Optics: Reflection (Mirrors)
Natural Virtual Images : “Mirages”
Light rays are observed as if they are
coming from the road’s surface
If the light is
bluish
(from blue
sky)
Mirage
appears blue,
like water
Lesson 1 of 1
Slide 3
Air is turbulent
due to heating
What is the “object” ??
Mirage
shimmers, as if
water waves are
present
A low section of the blue sky
Phys
311
Geometrical Optics: Reflection (Mirrors)
Lesson 1 of 1
Slide 4
Mirrors :
A mirror: is a surface that can reflect a beam of light in one direction instead of
either scattering it widely in many directions or absorbing it.
Example: a shiny metal surface.
How to draw
mirrors:
front
of
mirror
Back
of
mirror
Phys
311
Geometrical Optics: Reflection (Mirrors)
Types of Mirrors :
Planar
Mirrors
Spherical
Mirrors
Flat reflecting surfaces (also called plane mirrors).
Mirrors with curved surfaces which are in the shape
of a small section of the surface of a sphere.
Mirrors with curved surfaces which are in the shape
Aspherical
Mirrors
of a small section of the surface of a parabola,
ellipse, hyperbola, etc. rather than part of a sphere.
Lesson 1 of 1
Slide 5
Phys
311
Geometrical Optics: Reflection (Mirrors)
Types of Mirrors :
Concave
Mirrors
are spherical or aspherical mirrors which are
curving inwards “caved in”.
They are always converging in action.
are spherical or aspherical mirrors which are
Convex
Mirrors
curving outwards “flexed out”.
They are always diverging in action.
Lesson 1 of 1
Slide 6
Phys
311
Geometrical Optics: Reflection (Mirrors)
Types of Mirrors :
Lesson 1 of 1
Slide 7
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through a plane mirror :
𝒊 = −𝒑
Lesson 1 of 1
Slide 8
planar mirrors
Consider 2 rays:
Ob: perpendicular
to mirror.
Oa: with an angle
of incidence
(theta).
p = object distance from mirror. (p always positive).
i = image distance from mirrors. (i is negative because image is virtual).
Point
Objects
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through a plane mirror :
Group Work
Lesson 1 of 1
Slide 9
Point
Objects
In pairs, discuss:
Q: which rays reflected from a mirror result in seeing an image of a point object?
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through a plane mirror :
Each small portion of the object
acts like a point source.
Virtual image I has the same
Orientation & Height
as object O.
𝒊 = −𝒑
Lesson 1 of 1
Slide 10
planar mirrors
Extended
Objects
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through a plane mirror :
Mirror Maze
Lesson 1 of 1
Slide 11
Extended
Objects
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through a plane mirror :
Mirror Maze
Lesson 1 of 1
Slide 12
Extended
Objects
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through a plane mirror :
In pairs, discuss:
You are standing in the situation described by the
figure:
Each mirror produces a first (least deep) image
of the gargoyle (object O).
Then each mirror produces a second image with
the object being the first image in the opposite
mirror.
Then each mirror produces a third image with
the object being the second image in the
opposite mirror, and so on. You might see
hundreds of grinning gargoyle images.
Group Work
Lesson 1 of 1
Slide 13
Extended
Objects
Q: How deep behind mirror A
are the first, second, and third
images in mirror A?
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through Spherical Mirrors :
Centre of
Curvature
is the centre of the sphere of which
that mirror forms part of.
Radius of
Curvature
(r)
is the radius of the sphere.
Field of View
is the angular extent of object
space that can be observed or
embraced by an optical instrument.
Lesson 1 of 1
Slide 14
Phys
311
Geometrical Optics: Reflection (Mirrors)
Planar
Concave
Lesson 1 of 1
Slide 15
Convex
Type of
Mirror
Centre of
curvature
infinity
closer to the mirror,
and in front of it
Behind the mirror
Field of View
wide
Narrower (decrease)
Wider (increase)
Image distance
𝑖 = 𝑝
𝑖 > 𝑝
𝑖 < 𝑝
Image size
Same as object
Larger than object
Smaller than object
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through Spherical Mirrors :
Focal
point
Focal length
(f)
is a point to which parallel light rays, incident on a
curved mirror, converge (or appear to diverge).
is the distance of the focal point
from the centre of the mirror.
Q: Which is a positive quantity and
a negative quantity:
A. Real focal point :
B. Virtual focal point :
𝟏
𝟐
𝒇= 𝒓
Spherical
mirrors
Q: Do plane mirrors
have focal points?
Lesson 1 of 1
Slide 16
Phys
311
Geometrical Optics: Reflection (Mirrors)
Reflection through Spherical Mirrors :
Lesson 1 of 1
Slide 17
Group Work
In groups of 3:
Each group will be given a concave mirror, a ruler, and a small card.
Using these three tools, determine the position of the focal point and measure the
focal length.
Hint: place the small card at different distances from the mirror, a point image of an infinitely
distant object would appear on the card when the card is placed at the focal point.
Phys
311
Lesson 1 of 1
Slide 18
Geometrical Optics: Reflection (Mirrors)
𝟏
𝟏
+
𝒑
𝒊
Reflection through Spherical Mirrors :
For a planar mirror: (r  infinity) 
𝟏
𝟏
+𝒊
𝒑
=
𝟐

∞
𝟏
𝒇
𝟐
𝒓
= = Spherical mirrors
𝑝 = −𝑖
For a convex or planar mirror:
Only virtual images can form, regardless of the object’s position.
Image has the same orientation as the object.
For a concave mirror:
Both virtual and real
images can form,
depending on the
object’s position.
Phys
311
Geometrical Optics: Reflection (Mirrors)
How to easily draw rays with a spherical mirror:
Concave
Mirrors:
4 rays
Convex
Mirrors:
Lesson 1 of 1
Slide 19
Phys
311
Geometrical Optics: Reflection (Mirrors)
Lesson 1 of 1
Slide 20
Lateral Magnification :
The lateral magnification is determined by one of the following equations:
𝒊
𝒎=−
𝒑
𝒉′
𝒎 =
𝒉
where ℎ and ℎ′ are the heights of
the object and its image (measured
perpendicular to the central axis),
respectively.
When m is positive  object and image have the same orientation.
When m > 1  image > object.
When m < 1  image < object.
Phys
311
Lesson 1 of 1
Slide 21
Geometrical Optics: Reflection (Mirrors)
Reflection through spherical mirrors :
Group Work
In pairs: Go back to your notes and fill the table:
Mirror
Type
Object
Location
Image
Plane
Anywhere
Concave
Inside F
Location
Type
Sign
Orientation
of f
of r
of m
Outside F
Convex
Anywhere
Image on the same
side as object? Or
opposite side of
mirror?
Image
virtual?
or real?
Image same
as object?
Or
inverted?
You will need this
info to tackle
H.W. and tests
Sign: give the sign of
the quantity ( + ) or ( - )
? Fill in (+/-) if the sign
is ambiguous.
Phys
311
Geometrical Optics: Reflection (Mirrors)
Lesson 1 of 1
Slide 22
Exercise :
A tarantula of height h sits cautiously before a spherical mirror whose focal
length has absolute value | f | = 40 cm. The image of the tarantula produced by
the mirror has the same orientation as the tarantula and has height h' = 0.2h.
Q: (a) Is the image real or virtual, and is it on the same side of the mirror as the
tarantula or the opposite side?
What we know about the image:
If we go back to the table which we filled:
Because the image has the same orientation
as the tarantula (the object),it must be
virtual
and
on the opposite side of the mirror.
Phys
311
Exercise :
Lesson 1 of 1
Slide 23
Geometrical Optics: Reflection (Mirrors)
𝒊
𝒎=−
𝒑
𝒉′
𝒎 =
𝒉
𝟏
𝟏
+
𝒑
𝒊
𝟏
𝒇
𝟐
𝒓
= = Spherical mirrors
A tarantula of height h sits cautiously before a spherical mirror whose focal
length has absolute value | f | = 40 cm. The image of the tarantula produced by
the mirror has the same orientation as the tarantula and has height h' = 0.2h.
Q: (b) Is the mirror concave or convex, and what is its focal length f, sign
included?
We know that the image is virtual
Spherical mirror can be convex or concave
No use although, if we knew the sign of f 
we will know if it is convex or
concave.
How to know the sign of f ?? Check all available equations
We do not know if the focal point is real or virtual
We have information about the heights
Use magnification equation
Phys
311
Exercise :
Lesson 1 of 1
Slide 24
Geometrical Optics: Reflection (Mirrors)
𝒊
𝒎=−
𝒑
𝒉′
𝒎 =
𝒉
𝟏
𝟏
+
𝒑
𝒊
𝟏
𝒇
𝟐
𝒓
= = Spherical mirrors
A tarantula of height h sits cautiously before a spherical mirror whose focal
length has absolute value | f | = 40 cm. The image of the tarantula produced by
the mirror has the same orientation as the tarantula and has height h' = 0.2h.
Q: (b) Is the mirror concave or convex, and what is its focal length f, sign
included?
𝒉′ 𝟎. 𝟐𝒉
𝒎 = =
= 𝟎. 𝟐 Object and image have the same orientation  m is positive.
𝒉
𝒉
𝒊
𝒎 = +𝟎. 𝟐
→ 𝒊 = −𝟎. 𝟐𝒑
+𝟎. 𝟐 = −
𝒑
Do I need to
know what a
tarantula is ??
𝟏 𝟏 𝟏
𝟏
𝟏
𝟏
−𝟎. 𝟐
𝟏
because p is always positive
𝟏
𝒇=− 𝒑
= + =
+ =
+
= −𝟒
𝟒
 f is negative
𝒇 𝒊 𝒑 −𝟎. 𝟐𝒑 𝒑 −𝟎. 𝟐𝒑 −𝟎. 𝟐𝒑
𝒑
𝒇 = −𝟒𝟎 𝒄𝒎
 mirror is convex.
Phys
311
Geometrical Optics: Reflection (Mirrors)
Lesson 1 of 1
Slide 25
Homework :
Q1: True or false: Virtual images only form from reflection. Refraction always forms real images.
Q2 : Can we consider a plane mirror to be a spherical mirror?
Q3: A penguin waddles along the central axis of a concave mirror, from the focal point to an
effectively infinite distance. (a) How does its image move? (b) Does the height of its image
increase continuously, decrease continuously, or change in some more complicated manner?
Q4: You look through a camera toward an image of a hummingbird in a plane mirror. The camera
is 4.30 m in front of the mirror. The bird is at camera level, 5.00 m to your right and 3.30 m from
the mirror. What is the distance between the camera and the apparent position of the bird's image in
the mirror?
Phys
311
Geometrical Optics: Reflection (Mirrors)
Lesson 1 of 1
Slide 26
Homework :
Q5: Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation, each row in the
table gives object distance 𝑝𝑠 , (centimeters), the type of mirror, and then the distance (centimeters, without proper
sign) between the focal point and the mirror. Find (a) the radius of curvature r (including sign), (b) the image
distance i, and (r) the lateral magnification m. Also, determine whether the image is (d) real (R) or virtual (V), (e)
inverted (I) from object O or noninverted (NI), and (f ) on the same side of the mirror as O or on the opposite side.
Phys
311
Geometrical Optics: Reflection (Mirrors)
Homework :
Q6:
Lesson 1 of 1
Slide 27
Phys
311
Geometrical Optics: Reflection (Mirrors)
Lesson 1 of 1
Slide 28
Homework :
Q7: Locate the image of a paperclip 100 cm away from a convex spherical mirror having a radius of
curvature of 80 cm.
Q8: Design an eye for a robot using a concave spherical mirror such that the image of an object 1.0 m
tall and 10 m away fills its 1.0-cm-square photosensitive detector (which is movable for focusing
purposes). Where should this detector be located with respect to the mirror? What should be the focal
length of the mirror? Draw a ray diagram.
Phys
311
Geometrical Optics: Reflection (Mirrors)
Lesson 1 of 1
Slide 29 (last)
Summary:
Reflection through mirrors:
Images: real and virtual.
Mirrors: planar, spherical, aspherical.
Next lesson will cover:
Refraction
through lenses
Mirrors: convex and concave
Reflection through mirrors.
Object distance, image distance and orientation, and
focal length.
Lateral magnification.
Any Questions?