Important Formulas: Ray Optics

 Page 1


1 Re
ection of Light
Laws of re
ection:
normal
incident re
ected i
r
(i)
Incident ray, re
ected ray, and normal lie in the same
plane (ii)\i =\r
Plane mirror:
d d
(i) the image and the object are equidistant from mir-
ror (ii) virtual image of real object
Spherical Mirror:
O
I
u
v
f
1. Focal length f =R=2
2. Mirror equation:
1
v
+
1
u
=
1
f
3. Magnication: m =
v
u
2 Refraction of Light
Refractive index:  =
speed of light in vacuum
speed of light in medium
=
c
v
Snell's Law:
sini
sinr
=
2
1
1
2
incident
refracted
re
ected
i
r
Apparent depth:  =
real depth
apparent depth
=
d
d
0
O
I d
d
0
Critical angle: 
c
= sin
1 1

c

Deviation by a prism:


i i
0
A
r
r
0
 =i +i
0
A; general result
 =
sin
A+m
2
sin
A
2
; i =i
0
for minimum deviation

m
= ( 1)A; for small A
i

m
i
0
Refraction at spherical surface:
P O Q
1 2
u v

2
v


1
u
=

2

1
R
; m =

1
v

2
u
Lens maker's formula:
1
f
= ( 1)
h
1
R1

1
R2
i
Lens formula:
1
v

1
u
=
1
f
; m =
v
u
f
u v
Power of the lens: P =
1
f
, P in diopter if f in metre.
Two thin lenses separated by distance d:
1
F
=
1
f
1
+
1
f
2

d
f
1
f
2
f1 f2
d
3 Optical Instruments
Simple microscope: m =D=f in normal adjustment.
Compound microscope:
O 1
Objective Eyepiece
u v fe
D
1. Magnication in normal adjustment: m =
v
u
D
fe
2. Resolving power: R =
1

d
=
2 sin

Astronomical telescope:
fo fe
1. In normal adjustment: m =
fo
fe
, L =f
o
+f
e
2. Resolving power: R =
1


=
1
1:22
4 Dispersion
Cauchy's equation:  =
0
+
A

2
; A> 0
Dispersion by prism with small A and i:
1. Mean deviation: 
y
= (
y
 1)A
2. Angular dispersion:  = (
v

r
)A
Dispersive power: ! =
vr
y1


y
(if A and i small)
Dispersion without deviation:


0
A
A
0
(
y
 1)A + (
0
y
 1)A
0
= 0
Deviation without dispersion:
(
v

r
)A = (
0
v

0
r
)A
0