23 pius augustine reflection plane and spherical mirrors

1
Reflection: Plane and Spherical Mirrors

Reflection of light at plane surface
Dr. Pius Augustine, SH College, Kochi

Optics – Deals with behavior of light and other
electromagnetic waves
When wavelength of light is negligible compared
with the dimension of the device (mirrors, lenses
etc) light beam can be treated as a ray whose
propagation is governed by geometric optics)

Beam of light: Collection of rays of light is called
beam
Parallel beam
Divergent beam
Convergent beam

Reflection of light
The return of light into the same
medium after striking a surface is
called reflection.
(Partially absorbed or transmitted
depending on the nature of the surface)

Reflection of light
Able to see objects because of reflection of light
Luminous bodies are directly seen
Non luminous bodies are seen, because it reflect
incident light.
Different surfaces reflect light to different extents.
A smooth surface such as plane mirror reflects almost
the entire light incident on it.
A plane mirror is made by silvering on glass –
Silvered surface and Reflecting surface

Terms related with reflection
Incident ray
Point of incidence
Reflected ray
Normal
Angle of incidence
Angle of reflection
Plane of incidence
Plane of reflection
Real image
Virtual image

Plane of incidence (incidence plane or meridional plane)
Plane which contains the surface normal and incident ray
Plane of reflection
Plane on which the incident ray and the reflected ray lie

Real Image: Image which can be obtained on a screen
Obtained when light rays after reflection actually meet
Virtual image: cannot be obtained on a screen
Light after reflection donot actually intersect, but appear to
diverge from it.
By reproducing backward it can be made to intersect
(geometrically)

Retroreflection
The structure of these surfaces
are such that light is returned in
the direction from which it came
Eg. Corner reflection

Analyze dinner table optics
Spoon reflection
Wine glass reflection etc.

Kinds of reflection
1. Regular reflection or smooth or specular reflection
2. Irregular or diffuse or scattered reflection
In regular reflection, parallel beam of light after reflection also proceed
as parallel beam

Irregular reflection
Reflection from walls of a room, from a book page, etc.
Even a smooth surface, if examined in microscope, will be
uneven. (having projections)
When light rays hit different parts of a rough surface, rays are
reflected in many different directions – diffuse reflection
(irregular reflection)
Individual rays obey laws of reflection
Overall image is diffused
We can see object around us due to diffuse reflection

‘Albedo’ of an object is the extent to which it
diffusely reflect light from the sun (reflectivity)
Derived from the latin word albus (meaning
white)
Terrestrial and astronomical albedo

Laws of Reflection
1. Angle of incidence is equal to
angle of reflection
2. Incident ray, reflected ray and
normal at the point of incidence
lie on the same plane.
3. Light path are reversible
*When you see someone’s eyes in a mirror, he can also see you

It is a partially transparent mirror – separating a
dark room from bright room.
For bright room it act as mirror and for dark room it
act as transparent glass.
If light in the dark room is turned off and a flash
light is send to it, hidden chamber will be visible
What is one way mirror? How does it work?

Try this
1. Two plane mirrors M1 and M2 are inclined at θ. A
ray parallel to one mirror M1 strikes M2 and after
two reflections, emergent ray is parallel to M2.
Find θ ? (Ans: 60o)
2. At what angle should two plane mirrors be
inclined so that a ray incident on one mirror
parallel to the other mirror goes back along
original path after reflection form both the
mirrors. (Ans: 45o)

Practice image formation in the
case of extended objects

Lateral inversion
The interchange of the left and right sides in the object
and image in a plane mirror is called the lateral
inversion or mirror writing.
In mirror – inversion is only front to back
No left-right and up-down inversion

Lateral inversion
Letters A, H, I, M, O, T, U, V, W, X and Y – lateral
inversion is not noticeable.
Letters on the front of AMBULANCE
1 in 6500 inherited left hand writing
Leonardo davinci did most of his writing in ‘mirror’. He was a
left hander. To protect from theft and hide from church.
True purpose is still unknown. May be he was just learning.

Characteristics of the image formed by a plane mirror.
1.Upright
2.Virtual
3.Same size as the object
4.Laterally inverted
Image is situated a the same perpendicular distance
behind the mirror as the object is in front of it.

Relative speed of image as the object is moving towards
or away from mirror
If object advance a distance ‘d’ towards mirro,
image will also aproch the mirror by ‘d’.
Distance between object and image decrease by
2d.
ie. if an object moves with a speed v towards (or
away) from a mirror, the image to him appear to
move with a speed 2v.

A man approaches a vertical plane mirror at
speed of 2 m/s. At what rate does he
approach his image?

A parallel beam of light strikes a
plane mirror. What is the angle of
deviation produced?
(Hint: angle between incident and reflected ray)

You read newspaper because of the light it
reflects. Then why do you not see even a faint
image of yourself in the newspaper?

What is the focal length of a plane mirror?
1/u + 1/v = 1/f
1/x + 1/-x = 1/f
0 = 1/f
f = infinity
Glancing angle: Angle between incident ray and the surface

The reflected ray from a rotating plane mirror is
turning at the rate of 24o/sec. How many times is
the mirror rotating per minute?
A candle 4 cm tall is 36 cm to the left of a plane
mirror. Where does the mirror from the image
and what is the height of this image?

An object is placed midway between two parallel
mirrors, which will produce infinite number of
images. If x is the distance from the object to
either of the mirrors, find the distances of the
images from the mirror in terms of x?

An object is placed between two parallel mirrors
such that its distance to one of the mirrors is 3
times that to the other mirror. What is the
distance from the object to the image for each of
the five images that are closest to the object?

Suppose a mirror is rotated by an angle θ (say
anticlockwise), keeping the incident ray fixed then
the reflected ray rotates by 2θ along the same
sense, ie. anticlockwise.
Red – initial
Blue – after rotation

Number of images formed when two
mirrors are at angle θ
Multiple image formation
Object position can be either
symmetrical (θ1=θ2) or
assymmetrical (θ1 ≠ θ2)
Figure is showing an example for asymmetrical case.
There are different situations which we will see in the following
slides.

Case 1
If θ is such that 360/θ is an even number
(Both - object may be placed symmetrical or
asymmetrical w.r. to mirrors)
No. of images formed will be (360/θ) – 1
Eg. θ =60o, then 360/θ = 6
Then number of images = 5

Case 2 If θ is such that 360/θ is an odd number
Different situations should be taken separately
Situation 1
Object is placed symmetrical (θ1 = θ2)
No. of images formed will be (360/θ) – 1
Eg. θ =72o, then 360/θ = 5

Situation 2
Object is placed asymmetrical (θ1 ≠ θ2)
(Say 40o and 32o)
No. of images formed will be (360/θ)
Eg. θ =72o, then 360/θ = 5

Situation 1
360/θ is a fractional value eg.θ 75o.
360/θ = 4.8
(For both symmettrical and assymmetrical)
Number of images will be the completed whole
number (4)

Practice for different cases
Find out range of angles between two plane mirrors,
so that number of images formed = 3?
What is the minimum size of the mirror required for
a 6 ft tall person to be able to see a full length
image?

Q. Two mirrors are perpendicular to each
other. A ray travelling in a plane
perpendicular to both mirrors is reflected
from one mirror and then from the other.
What is ray’s final direction relative to initial?

Two mirrors are arranged perpendicular to
each other. Prove that for a ray of light which
undergoes reflection from both mirrors,
incident and receding rays will be parallel
(what ever may be the angle of incidence on
the first mirror).

Size of the mirror needed to see complete image
Q. Find the minimum length of the mirror that is need for a
person of height H to see his entire reflection.
Ans: H/2

A parallel beam of white light is allowed
fall on the wall and mirror inside a dark
room.
Will you be able to see the reflected light
from anywhere in the room in the above
two cases. Comment.
Hint: Specular and Diffuse reflections

Uses of Plane Mirrors
1. Personal grooming
2. Optitian’s room (to increase the effective length of the
room)
3. Barber shops
4. Periscope
5. Kaleidoscope
6. Solar cooker
7. Scientific appliances

An object is kept at a distance of 15 cm from a plane
mirror. Mirror is moved 5 cm towards the mirror and
simultaneously object is moved 2 cm away from the
mirror.
Find i) the distance between the new positions of
the image and object? ii) distance between old
position of the object and new position of the image?

Why are reflected images are seen more
easily at night in a window from inside of
the house, while during day time they are
not?

Metal alloy, front surface reflecting mirror
eliminates secondary reflections and
aberrations of back surface reflecting mirror.
Cu+Sn Alloy (not sure)

Mirror Writing Exercise!!
Write longest english word (medical term) (lateral inversion)
Crazy!!!!

Longer the mirror, brighter will be the image. Do
you agree? Support your answer with necessary
diagrams.

Spectrophobia-Fear of Mirrors
A man holding a lighted candle in front of
a thick glass mirror and viewing it
obliquely sees a number of images of the
candle. What is the origin of the multiple
images?

Spherical Mirrors

Spherical Mirrors:
A mirror of which the reflecting surface is
a part of a sphere is called a spherical
mirror
Note:
A mirror having parabolic section is called
parabolic mirror
Curved mirror can be spherical or cylindrical

Concave Mirror Convex Mirror

Concave mirror?
It is a spherical mirror in which
the reflection of light takes place
at the bent in surface.

Convex mirror?
It is a spherical mirror in which the
reflection of light takes place at the
bulging out surface.

Radius of curvature of a spherical mirror?
It is the radius of the hollow sphere of
which the mirror forms a part.

Pole of spherical mirror
The centre or middle point of a
spherical mirror is called its pole.

Principal axis of a spherical mirror
The straight line passing through the centre of
curvature and pole of a spherical mirror is
called its principal axis.

Aperture of spherical mirror
The portion of a mirror from which reflection
of light actually takes place is called the
aperture of the mirror.
Portion of the mirror exposed to light
AB
linear aperture
Angle ACB
angular aperture

Principal section of the mirror
A section of a spherical mirror cut by a
plane passing through the pole and
the centre of curvature of the mirror

Principal focus of a spherical mirror
It is a point on its principal axis to which all the
light rays which are parallel and close to the axis
converge after reflection from the concave
mirror and diverge after being reflected from
the convex mirror.

A beam of light parallel and close to the principal
axis after reflection from the concave/convex
spherical mirror converges or appears to diverge
to/from a fixed point on the principal axis. This fixed
point is called principal focus of concave/convex
mirror.

Ray of light (AB) parallel to principal axis falling on the
spherical mirror at B, after reflection passing through F.
Triangle CFB is isosceles.
So CF = FB =FP = focal length
B is close to P from definition of principal focus
CP = R R = 2f
Angle i = angle θ (alternate angles)
Angle i = angle r (law of reflection)
Show that R = 2f

Repeat for convex mirror to show that R = 2f

Obtain image position for parallel
beam of light not parallel to principal
axis falling on concave spherical
mirror.

Focal plane is a plane perpendicular to
principal axis passing through principal focus,
on which parallel rays after reflection
converges.
Each point on the focal plane is called focus of
mirror.
Principal focus is one of the points on the
focal plane on the principal axis.

Spherical Aberration

Spherical Aberration
If a wide beam of light is allowed on a spherical
mirror of large aperture, paraxial rays converge
to principal focus, where as marginal rays will
be converged to a point closer to the mirror than
the principal focus, due to which image formed
will be blurred.

Note:
Hubbles space telescope showed error in 1990
due to spherical aberration (diameter = 2.4 m)
1992 corrective measures were applied
Corrective measure: using stops to prevent
marginal rays from falling on the mirror.

A concave spherical mirror of f = 15
cm is immersed in water. What
change do you expect in the focal
length?
No change

Practice drawing before proceeding

Convenient rays to locate image
Practice drawing…

Different rays for locating images

Sign conventions
i. Light is incident on the mirror from the left
hand side of the mirror.
ii. All distances are measured from pole
iii. Distance in the direction of incident light is
taken as +ve and opposite is –ve.
iv. Height measured upward is +ve and
downward is –ve.

A ray from the object that is parallel to
the principal axis will be reflected
through the focal point

A ray from the object through the focal point will be
reflected parallel to the principal axis

A ray from the object along a radius will be reflected
back along the radius

A ray (dashed) to the mirror center (P) will be
reflected at an equal and opposite angle

Image formation
Object position between C and F

Image formation
Object position between F and pole

Draw ray diagrams for the following
object positions
1.Beyond C
2. At C
3. Between F and C
4. At F
5. Between F and P

Windows of some department store,
rather than being vertical, slant
inward at the bottom. Explain.

A person in a dark room looking
through a window can clearly see a
person outside in the daylight, whereas
the person outside cannot see the
person inside. Give reason.
Hint: act like one way mirror.

What is the advantage of having
matte (nonglossy) pages in the
book rather than pages with a
glossier surface?
Diffuse reflection is preferred

Why is it difficult to see the
roadway in front of you when
driving on a rainy night?

Which kind of road surface is easier
to see when driving at night-
pebbled, uneven surface, or a
mirror smooth surface ?

Paradox:
Why does a mirror reverse left and right
when it does not reverse up and down?
A mirror reverses neither left and right nor up
and down. It reverses front and back. This has
the effect of making a left hand into a right
hand, and vice versa.

Newton’s formula
Instead of measuring distance from poles, if
measured from ‘f’ as
a - to object
b – to image
Then f2 = ab
Prove this result?

Can we use a ray passing through centre of
curvature, for locating image when object is at C?
Note: possible if object is point object on principal
axis.
Image of an erect object (previous slides) is located
when the image positions of its two extreme ends are
located. In the earlier diagrams, one end was on
principal axis and was located without drawing
(assumed)

Define real image and virtual image?
Image formed by actual intersection of
reflected light rays is called a real
image.
Apparent intersection of reflected
light rays - virtual image

Name the spherical mirror which has
i) real principal focus ii) virtual
principal focus
Real -- concave mirror
Virtual – convex mirror

How is an image formed ?
An image is formed at a point
where reflected rays intersect
(or appear to intersect)
To locate – use at least two rays

For what position of an object, a
concave mirror forms a real image
equal in size to that of object ?
At center of curvature C

For what position of an object, a concave
mirror forms an enlarge virtual image
between the pole and focus.

Where should an object be placed in front
of a concave mirror so as to obtain its
magnified erect image?
Between pole P and focus F

Locate image positions for point object
Concave Mirror.
1 beyond C
2 at C
3 between F and C
4 At F
5. between F and P

Magnification
i. Lateral or transverse magnification = hi/ho
ii. Axial or longitudinal magnification = -di/d0 = -v/u
iii. Angular magnification = sinθ’/sinθ
iv. Areal magnification = Area of image/area of object
1/v + 1/u = 1/f
1/di + 1/do = 2/R

Find the distance of object from a concave mirror of focal
length 10 cm so that image size is four times the size of the
object.
Hint:
Two cases – image is real and image is virtual
Case – 1 Real
u = -x v = -4x f = -10 cm
Solve 1/v + 1/u = 1/f x =12.5 cm
Case 2 Image is virtual
u = -y v = 4y f = -10 cm
Solve 1/v + 1/u = 1/f x = 7.5 cm

How far should an object be from a
concave spherical mirror of radius 36
cm to form a real image one-ninth its
size?

If an object is placed at the focus
of a concave mirror, then where is
the image formed ?
inifinity

Why does a driver prefer to use a
convex mirror as rear view mirror
in an automobile ?
Convex mirror has a wider field
of view.

Write 3 uses of a concave mirror
i. Shaving mirror
ii. Reflectors in car head lights.
iii. Doctors head mirrors

i. At focus
ii. Between F and C
iii. At C
iv. Beyond C
v. at infinity.
For which position of the object does a concave mirror
produce an inverted, magnified and real image

Position of the
object
Position of the
image
Nature and size
of the image
Use
At infinity At the focus Real, inverted
and diminished
Collector of
radiation in solar
heating
Beyond C Between F and C Real, inverted
and diminished
In flood lights
At C At C Real, inverted
and same size
Between C and F Beyond C Real inverted and
magnified
At F At infinity Real, inverted
and magnified
Reflecting mirror in
car head lights,
search lights.
Between F and P Behind the mirror Virtual, erect and
magnified
As a shaving mirror
or make up mirror
and dentists
mirror.

Explain the movement of image
as the object is moving from
infinity towards the concave
mirror

As the object is moving from infinity
towards the focal point , real image is
moving from ‘f’ to infinity
After which as the object further
moves towards the pole, virtual image
is moving from infinity towards the
mirror

Give the position of the
object in front of a concave
mirror for which image can
be real as well as virtual.
Explain with ray diagram.

Locate the image for a point object
located on the principal axis in the
following cases.
i. between F and P
ii. At F
iii. Between F and C
iv. At C

An object is placed on the
principal axis in front of a concave
mirror in such a way that , half of
the object is between F and P and
half beyond F . Locate the image

If an object is moving with constant
velocity from infinity towards the
focal point of a concave mirror, will
the image be moving with uniform
velocity . Explain.

An object is moving from f to P
and f to c (in an identical manner)
in front of concave mirror. Will
the image velocity in the two cases
be equal ?

Convex Mirror – Image formation
Image is between F and pole P on other side of
the mirror Virtual, Upright and Diminished
Object at infinity – image at f

Concave mirror – solar concentrator or solar cooker
Solar light coming from infinity (parallel rays) will be
concentrated to focal point.
Cooker at F will receive heat.

Uses of concave mirror – Dentist mirror
Tooth will be brought between f and p of
concave mirror, a magnified, erect virtual
image is formed within the mirror – which
gives a better examination.

Uses of concave mirror – as shaving mirror
Face is between f and p of concave mirror, a
magnified, erect virtual image is formed within
the mirror.
Concave mirror of large focal length is used so that
face can be easily maintained between f and pole

Concave mirror as search light reflector
Bulb at focal point of concave mirror. Parallel beam
of light will be produced.
Automobiles, cycles, torch light etc.

Concave mirror as Doctor’s head mirror
Light from patient’s side will be focused on the
patient like a torch light for better visibility

A point object is placed in front
of a convex mirror at distance
equal to its focal length. Locate
the image

Convex mirror – uses
i. As rear view
mirror.
ii. As reflector in
street lights.
Bulb

Rear view mirror

Identifying mirror without touching
Plane: image upright and same size.
Mirror moves towards or away from object, no change
in size of image.
Concave: image is upright and magnified.
Image becomes inverted on moving the mirror away
from face.
Convex : image is always upright and diminished.

Draw virtual images formed by the plane
mirror, concave mirror and convex
mirror and compare the nature and
property of the images?

Difference between concave and convex mirrors
Concave
i. Silvering - outside
ii. Reflection – inside
iii. Converges light
iv. Real as well as
virtual image
v. Magnified, same
size as well as
diminished image.
Convex
i. Silvering - inside
ii. Reflection –
outside
iii. Diverges light
iv. Virtual image only
v. Diminished image
only

A few questions from shadows

Hot and cold light sources
Hot - electric bulb, sun, stars,
thermonuclear reactions
Cold - fluorescence tube light ,
firefly

Why are circular patches of light is seen
under a tree during day time?
In between overlapping leaves of a tree, there are
always, small spaces which act like pinholes.
Each pin hole forms the image of the sun on the
ground.
Large number of such images overlap and form
blurred images which appear as oval patches of
light.

Can we look at the sun or solar eclipse
directly with the naked eye ? Why?
No,
Rays coming from the sun are very strong in
an eclipse, which can damage our eyes .
Use plane black glass to see sun or image.
Or use pinhole camera.

Differentiate between luminous and non
luminous objects. Give ex.
Luminous – emit light of their own.
Eg. Sun, burning candle, fluorescent tube,
electric bulb.
Non luminous – do not emit their own light
but become visible by light incident from
some luminous objects on them.
Eg. Table, moon, earth.

Why does a bird flying in the air not cast
a shadow?
If the object is much smaller than the
source of light, umbra (perfectly dark
shadow) completely vanishes.

What do you mean by earth light?
It is the light of the sun reflected from the surface of
the earth .
Eg. Immediately following the new moon day,
crescent moon is observed on the western
horizon, just after sunset.
Crescent is the portion of the moon which is
illuminated by sunlight while the rest of the
moon visible faintly is illuminated by light
reflected from the earth.

What will be the effect on the image due to a wide
pinhole ?
Equivalent to a large number of
small holes, each small hole
produces its own image at a slightly
different place.
Image will be blurred.

If you have to measure the height of a
tree without climbing it , what method
will you follow ? Explain.

For my youtube videos: please visit -
SH vision youtube channel
or
xray diffraction series
SH Vision

135
Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
we will
overcome
Thank You
http://piusaugustine.shcollege.ac.in
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Dr. Pius Augustine, Asst. Professor, Sacred Heart College, Thevara, Kochi.

23 pius augustine reflection plane and spherical mirrors

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