Ray optics complete summary and formulas

Simple Microscope
1. Image formed at infinity
Compound Microscope

Ray Optics Optical Instrument h
I

F

V
h
O

u
β
C
F
MP =
−v  D 
 
u  f0 

2. Image formed object lens
v0 ue
eye lens

B object
1. Image formed at infinity h F0 A’ C
D −v  D A F0 C A’’
MP = at near point MP = 1 + 
h1
u  f0 




final image
f
Laws of Reflection 2. Image formed at near point
D
u0


B’’
h2

ve=L
B’


MP = 1 +
f


Spherical Mirrors Apparent death =
Re al death
K
N Astronomical Telescope
1. The incident ray reflected ray and n
normal to the reflecting surface all TIR  1 Air
1. Image formed at infinity
−f
f0

Normal shift = d  1 −  P A B Q fe
MP = 0
lie in same plane.
The bouncing back of light ray in the  n Apparent
depth u0 R




Water
F0 A Fe
2. Angle of reflection is always equal to Mirror formula where d is real depth.
Real
depth Normal 2. Image formed at near point
α
O
A
α
1
β
β


same denser medium after reflection shift
angle of incidence, i.e.,
∠i=∠r
B1
−f  f 
1 1 1 MP = 0 1 + e 
O N
from an interface with a rarer medium ue
fe  D 
= +
B
is termed as boral internal reflection. ve



f u v Total internal
reflection


i r In proper sign convention. In person sign convention
Prism A
v M
µ1 i µ2

Object Focal
Angle of deviation δ = i + e – A
Point
Principal Pole
i r α θ
C
L




axis Image O P N I
GLE
OF
AN VIATIO
N R
M
DE
u v
Mirror
δ




Sign Convention f TR
AY
i1
P



r1
δ1 δ2



r2
Q



i2



EM
E
RA RGE
Y NT
B


µ 2 µ1 µ 2 − µ1
N
IDE
INC
u
N




− =
R
B C

O




v u R
Critical Angle For minimum deviation
1. i = e




Refraction from spherical surface
1. All distances are measured from Linear magnification
the pole and is the origin.
const.
A In proper sign convention
It is the angle of incidence for which the 2. r =
2
2. Distances measured to the right of angle of incidence is 90°.
X
min  sin+ A  A
the pole are taken as positive. sin   B

3. µ =  2  µ
3. Distance above the principal axis are Critical angle
i A
µ
i=e
taken as positive. sin   O C2 C1 I I1
A 2 R1

−1  n2 R2 v1
4. Angle measured from the normal in B1 C o u v

the anti-clockwise direction are B F P r = 90⁰
θc = sin  
 n1 
Y
u
For thin prism,
A

positive. I
Incident + θc
1  1 1 
= (µ − 1)  − 
Ray A1 v δ = (µ – 1) A δ f  R1 R2 


I −v Lens formula
m= =
- +



O u Conditions for TIR h0
-
∞ 2F F O F 2F I ∞
o
In proper sign convention 1. The light ray must travel from denser Dispersion through Prism hi
to rarer medium. u v
Absolute Refractive Index 2. The angle of incidence must be greater When white light passes through the prism,
1 1 1
Longitudinal magnification than the critical angle. then it splits into its seven constituent = −
f v u
colours. This phenomena of splitting of In person sign
It is defined as ratio of speed of light in h′ v
white light is known as dispersion of light. m= = convention
vacuum to speed of light in medium h u
i.e n = c
v image
object Application of TIR
Power of lens
u2 u1
v2 It is defined as the reciprocal
v1 1. Sparkling of diamond
2. Optical Fibre of focal length of metres, i.e.,
Laws of Refraction v 2 − v1 3. Mirage and optical looming.
mL =
1. The incident ray, refracted ray and u2 − u1
normal to the interface of two media
all lie on the same plane.
For small objects, mL = m2 Scattering
Scatt
ere
d lig
ht
P=
1
=
100
f(m) f(cm)
2. Snell's law µ2 sin r = µ1 sin i Compound Lens


The deflection of light ray by the fine
particles of matter is known as For combination of lenses,
Air Superficial Magnification scattering of light. P = P1 + P2
ra




r
ed
ct




1 1 1
ms = ma × mb For small objects, mL = m2
n
fra
Re




n
From Ray Leighscattering, I ∝ 1 = +
f f1 f2
y




a×b
a
nt r




λ4
ide




Water i
b Observer
=m 2 mb where λ is wavelength of light and I is intensity of light.
Inc




a
ma In proper sign convention


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