704
15 Optics
Fibre optics: The maximum acceptance angle θ max outside which entering rays
will not be totally reflected within the fibre is given by
n 0 sin θ max =
n 2
f − n 2
c
(15.5)
where n 0 is the refractive index of the medium outside the fibre, n f that of the fibre
and n c that of the cladding material.
Snell’s law of refraction
n 1 sin i = n 2 sin r
(15.5a)
where i = angle of incidence and r = angle of refraction.
Prisms (Fig. 15.1)
Fig. 15.1
r 1 + r 2 = A
(15.6)
δ = (i 1 − r 1 ) + (i 2 − r 2 ) = i 1 + i 2 − A
(15.7)
For minimum angle of deviation
δ = D, i 1 = i 2 , r 1 = r 2
(15.8)
n = sin
1
2
(A + D)/ sin
1
2
(A)
(15.9)
If the prism of index n 1 is placed in a medium of index n 2 then n should be replaced
by n 1 /n 2 .
Lenses: Object distance (u), image distance (v) and focal length ( f )
1
u
+
1
v
=
1
f
(15.10)
15 Optics
Fibre optics: The maximum acceptance angle θ max outside which entering rays
will not be totally reflected within the fibre is given by
n 0 sin θ max =
n 2
f − n 2
c
(15.5)
where n 0 is the refractive index of the medium outside the fibre, n f that of the fibre
and n c that of the cladding material.
Snell’s law of refraction
n 1 sin i = n 2 sin r
(15.5a)
where i = angle of incidence and r = angle of refraction.
Prisms (Fig. 15.1)
Fig. 15.1
r 1 + r 2 = A
(15.6)
δ = (i 1 − r 1 ) + (i 2 − r 2 ) = i 1 + i 2 − A
(15.7)
For minimum angle of deviation
δ = D, i 1 = i 2 , r 1 = r 2
(15.8)
n = sin
1
2
(A + D)/ sin
1
2
(A)
(15.9)
If the prism of index n 1 is placed in a medium of index n 2 then n should be replaced
by n 1 /n 2 .
Lenses: Object distance (u), image distance (v) and focal length ( f )
1
u
+
1
v
=
1
f
(15.10)