Geometry of image formation

discussing here…......

mirrors

aspects of plane mirror

definition of mirror

aspects of curved mirrors

types of mirrors

what is mirror ? glass sheet with silvery / metallic coating at the back

mirror

curved plane

curved mirror

concave convex

explanation:

real vs. virtual image (by reflection)

real vs. virtual image (by reflection)

virtual image real image

forms in locations, where the light rays do NOT actually reach

emerging rays converge

forms in locations, where the light rays

actually reach

emerging rays diverge

no need for extrapolation by extrapolation, the light ray appears to be coming from the image

forms on the SAME side as the object forms on the OTHER side

can be projected onto a screen can NOT be projected onto a screen

image formation by PLANE mirror

correct Geometric drawing

reflected ray

the ray reflects back along the normal

incident ray

when the incident ray falls parallel to the normal

when the incident rays fall at acute angles

by backward extrapolation, all reflected rays converge to construct the image

N.B. : color codes

incident rays

emerged rays

extrapolations

plan

e m

irror

obje

ct im

age

∠ θi

∠ θr ∠ θi = ∠θr

a b

a = b

c d

c = d

image characteristics (plane mirror)

always behind the mirror

always virtual

always same size as the object

always at the same distance as the object

always upright

always left-right reversal

aspects of convex mirror

how to determine the focal point

Geometry of convex mirror

image formation by convex mirror

Geometry of convex mirror

convex mirror =

segment of spherical glass surface,

bulging side facing the light source (object)

convex mirror segment of spherical glass surface,

bulging side facing the light source (object)

principal axis

reflecting surface

center of curvature = 2F

focus

focal length F

how to determine the focal point of a convex mirror

focus

determination of focal point in CONVEX mirror pa

ralle

l inc

iden

t bea

m

backward extrapolation

guidelines for reflection by CONVEX mirror

correct Geometric drawing (convex mirror)

reflected ray

when the incident ray falls along the principal axis

the ray is reflected back along the principal axis

incident ray

correct Geometric drawing (convex mirror)

reflected ray

by backward extrapolation, reflected ray comes from the focus

incident ray

when the incident ray falls parallel to the principal axis

F

correct Geometric drawing (convex mirror)

reflected ray incident ray

when the incident ray is directed towards the focal point

the reflected ray emerges parallel to the principal axis

F

correct Geometric drawing (convex mirror)

reflected ray incident ray

when the incident ray is directed towards the point of curvature

reflected ray follows the same path back

C

image formation by CONVEX mirror

F C

convex mirror object beyond C

convex mirror

C F

object closer then C

F C

convex mirror object closer than F

object position image position image size nature of image

at infinity at F point virtual

between C and F

between F and mirror virtual and upright diminished

at C

between infinity and C

at F

between F and mirror

summary (convex mirror)

between F and mirror virtual and upright diminished

between F and mirror virtual and upright diminished

between F and mirror virtual and upright diminished

between F and mirror virtual and upright diminished

aspects of concave mirror

how to determine the focal point

Geometry of concave mirror

image formation by concave mirror

Geometry of concave mirror

concave mirror =

segment of spherical glass surface,

curved inwards

concave mirror segment of spherical glass surface,

curved inwards

principal axis

reflecting surface

center of curvature = 2F

F

how to determine the focal point of a concave mirror

focu

s

determination of focal point in CONCAVE mirror

para

llel i

ncid

ent b

eam

guidelines for reflection by CONCAVE mirror

correct Geometric drawing (concave mirror)

reflected ray

when the incident ray falls along the principal axis

the ray is reflected back along the principal axis

incident ray

correct Geometric drawing (concave mirror)

reflected ray

the reflected ray passes through the focal point

incident ray

when the incident ray falls parallel to the principal axis

F

correct Geometric drawing (concave mirror)

reflected ray incident ray

when the incident ray falls through the focal point

reflected ray emerges parallel to the principal axis

F

correct Geometric drawing (concave mirror)

reflected ray incident ray

when the incident ray falls through the point of curvature

reflected ray follows the same path back

c

image formation by CONCAVE mirror

concave mirror

F

c

object beyond C

concave mirror object at C

F c

F

concave mirror object between C and F

C

F

concave mirror object at F

F

concave mirror object between F and mirror

object position image position image size nature of image

at infinity at F point real

between C and F

between C and F real and inverted diminished

at C at C same size real and inverted

between infinity and C

beyond C enlarged real and inverted

at F no image

between F and mirror virtual and upright magnified behind mirror

summary (concave mirror)

https://en.wikipedia.org/wiki/Geometrical_optics

https://spie.org/

useful links

http://www.physicsclassroom.com/

http://hyperphysics.phy-astr.gsu.edu/

http://www.atoptics.co.uk/

https://www.boundless.com/physics/textbooks/boundless-physics-textbook/