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 f -p h y s i c s . c om | pg. 1
h i
1 1 1
1 Reflection of Light Lens maker’s formula: f = (µ − 1) R1 − R2
normal f
Laws of reflection: (i)
incident i r reflected 1 1
Lens formula: v − u = f1 , m= v
u
Incident ray, reflected ray, and normal lie in the same
plane (ii) ∠i = ∠r u v
Power of the lens: P = f1 , P in diopter if f in metre.
Plane mirror:
d d Two thin lenses separated by distance d:
(i) the image and the object are equidistant from mir-
ror (ii) virtual image of real object
1 1 1 d
= + − d
F f1 f2 f1 f2
I
f1 f2
Spherical Mirror: O
f
v
u
3 Optical Instruments
1. Focal length f = R/2
Simple microscope: m = D/f in normal adjustment.
1 1 1
2. Mirror equation: v + u = f
Objective Eyepiece
3. Magnification: m = − uv
O ∞
Compound microscope:
2 Refraction of Light
u v fe
speed of light in vacuum c
Refractive index: µ = speed of light in medium = v
D
v D
incident reflected
1. Magnification in normal adjustment: m = u fe
sin i µ2 µ1 i
Snell’s Law: sin r = µ1 2. Resolving power: R = 1
= 2µ sin θ
µ2 ∆d λ
r refracted
fo fe
real depth d d0
Apparent depth: µ = apparent depth = d0 d I
O Astronomical telescope:
Critical angle: θc = sin−1 1
µ
µ
θc
1. In normal adjustment: m = − ffoe , L = fo + fe
1 1
2. Resolving power: R = ∆θ = 1.22λ
A
δ
Deviation by a prism: i i0 4 Dispersion
r r0
A
µ Cauchy’s equation: µ = µ0 + λ2 , A>0
δ = i + i0 − A, general result Dispersion by prism with small A and i:
sin A+δ m
1. Mean deviation: δy = (µy − 1)A
µ= 2
A
, i = i0 for minimum deviation
sin 2 2. Angular dispersion: θ = (µv − µr )A
δ µv −µr θ
δm = (µ − 1)A, for small A Dispersive power: ω = µy −1 ≈ δy (if A and i small)
δm
i0 i
A µ0
Dispersion without deviation:
µ1 µ2 µ A0
Refraction at spherical surface: (µy − 1)A + (µ0y − 1)A0 = 0
P O Q
u v Deviation without dispersion:
(µv − µr )A = (µ0v − µ0r )A0
µ2 µ1 µ2 − µ1 µ1 v
− = , m=
v u R µ2 u
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c 2019 by Jitender Singh Ver. 2019 1
h i
1 1 1
1 Reflection of Light Lens maker’s formula: f = (µ − 1) R1 − R2
normal f
Laws of reflection: (i)
incident i r reflected 1 1
Lens formula: v − u = f1 , m= v
u
Incident ray, reflected ray, and normal lie in the same
plane (ii) ∠i = ∠r u v
Power of the lens: P = f1 , P in diopter if f in metre.
Plane mirror:
d d Two thin lenses separated by distance d:
(i) the image and the object are equidistant from mir-
ror (ii) virtual image of real object
1 1 1 d
= + − d
F f1 f2 f1 f2
I
f1 f2
Spherical Mirror: O
f
v
u
3 Optical Instruments
1. Focal length f = R/2
Simple microscope: m = D/f in normal adjustment.
1 1 1
2. Mirror equation: v + u = f
Objective Eyepiece
3. Magnification: m = − uv
O ∞
Compound microscope:
2 Refraction of Light
u v fe
speed of light in vacuum c
Refractive index: µ = speed of light in medium = v
D
v D
incident reflected
1. Magnification in normal adjustment: m = u fe
sin i µ2 µ1 i
Snell’s Law: sin r = µ1 2. Resolving power: R = 1
= 2µ sin θ
µ2 ∆d λ
r refracted
fo fe
real depth d d0
Apparent depth: µ = apparent depth = d0 d I
O Astronomical telescope:
Critical angle: θc = sin−1 1
µ
µ
θc
1. In normal adjustment: m = − ffoe , L = fo + fe
1 1
2. Resolving power: R = ∆θ = 1.22λ
A
δ
Deviation by a prism: i i0 4 Dispersion
r r0
A
µ Cauchy’s equation: µ = µ0 + λ2 , A>0
δ = i + i0 − A, general result Dispersion by prism with small A and i:
sin A+δ m
1. Mean deviation: δy = (µy − 1)A
µ= 2
A
, i = i0 for minimum deviation
sin 2 2. Angular dispersion: θ = (µv − µr )A
δ µv −µr θ
δm = (µ − 1)A, for small A Dispersive power: ω = µy −1 ≈ δy (if A and i small)
δm
i0 i
A µ0
Dispersion without deviation:
µ1 µ2 µ A0
Refraction at spherical surface: (µy − 1)A + (µ0y − 1)A0 = 0
P O Q
u v Deviation without dispersion:
(µv − µr )A = (µ0v − µ0r )A0
µ2 µ1 µ2 − µ1 µ1 v
− = , m=
v u R µ2 u
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c 2019 by Jitender Singh Ver. 2019 1
