Fo rm u l ae
S h e et fo r
O p ti c s
w w w .c o n c e p t s - o
1
f
Lens maker’s formula:
1 Reflection of Light
normal
Laws of reflection:
i r
incident
f -p h y s i c s . c om
h
= (µ − 1)
1
R1
−
1
R2
| pg. 1
i
f
(i)
reflected
Lens formula:
Incident ray, reflected ray, and normal lie in the same
plane (ii) ∠i = ∠r
1
v
−
1
u
= f1 ,
v
u
m=
u
v
Power of the lens: P = f1 , P in diopter if f in metre.
Plane mirror:
d
d
(i) the image and the object are equidistant from mirror (ii) virtual image of real object
I
Spherical Mirror:
Two thin lenses separated by distance d:
1
1
1
d
=
+
−
F
f1
f2
f1 f2
d
f1
O
f2
f
u
v
3 Optical Instruments
1. Focal length f = R/2
2. Mirror equation:
1
v
1
u
− uv
+
3. Magnification: m =
=
Simple microscope: m = D/f in normal adjustment.
1
f
2 Refraction of Light
Snell’s Law:
sin i
sin r
=
∞
O
Compound microscope:
u
speed of light in vacuum
speed of light in medium
Refractive index: µ =
Eyepiece
Objective
=
incident
µ1 i
µ2
µ1
µ2
v
c
v
fe
D
reflected
1. Magnification in normal adjustment: m =
2. Resolving power: R =
r
1
∆d
=
v D
u fe
2µ sin θ
λ
refracted
fo
Apparent depth: µ =
real depth
apparent depth
Critical angle: θc = sin−1
=
fe
d0
d
d0
d I
O
1
µ
Astronomical telescope:
µ
θc
1. In normal adjustment: m = − ffoe , L = fo + fe
2. Resolving power: R =
1
∆θ
=
1
1.22λ
A
δ
Deviation by a prism:
i
i0
r0
r
Cauchy’s equation: µ = µ0 +
µ
δ = i + i0 − A,
µ=
m
sin A+δ
2
,
A
sin 2
A
λ2 ,
i = i0 for minimum deviation
1. Mean deviation: δy = (µy − 1)A
2. Angular dispersion: θ = (µv − µr )A
for small A
Dispersive power: ω =
δm
i0
µv −µr
µy −1
≈
µ1
Refraction at spherical surface:
µ2
m=
(if A and i small)
A
µ0
µ
A0
(µy − 1)A + (µ0y − 1)A0 = 0
P
Q
O
u
µ2
µ1
µ2 − µ1
−
=
,
v
u
R
θ
δy
i
Dispersion without deviation:
Get Formulas
A>0
Dispersion by prism with small A and i:
general result
δ
δm = (µ − 1)A,
4 Dispersion
v
Deviation without dispersion:
(µv − µr )A = (µ0v − µ0r )A0
µ1 v
µ2 u
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c 2019 by Jitender Singh Ver. 2019
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