Geometrical Optics
Refraction through prism
Synopsis
1. Prism is a medium enclosed between two plane surfaces intersecting at some angle along a line.
The line of intersection of the two planes is called refracting edge and angle of intersection of the
two planes is called angle of the prismA. The two surfaces may or may not be actually
intersecting with each other. RI of the medium ‘n’ and angle of the prism ‘A’ are the two constants
of the prism
Refraction through a Prism:
A
r
r
=
+
2
1
;
(i
1
r
1
)+(i
2
r
2
) =
δ
δ
= (i
1
+i
2
A);
2
2
1
1
sinr
sini
sinr
sini
n
=
=
At position of minimum deviation (i
1
=i
2
=i) and (r
1
=r
2
=r=A/2), the ray traveling in prism is
parallel to its base and refractive index of the material of the prism is given by,
2
A
sin
2
δ
A
sin
sin
sin
n
m
+
=
=
r
i
For maximum deviation either
0
2
0
1
90
i
or
90
i
=
=
For thin prism ‘A’ is small of the order 8
0
to 10
0
:
A
n
)
1
(

=
δ
Special Cases:
(A) For normal incidence (i
1
=0
0
), r
1
=0
0
and
r
2
=A. Let C be the critical angle of the materialof the
medium
If (r
2
=A)<C ray emerges; If (r
2
=A)=C the emergent ray grazes the second surface; If
(r
2
=A)>C ray does not emerge from the prism due to TIR
(B) For grazing incidence (i
1
=90
0
), r
1
=C and
r
2
=AC
If (r
2
=AC)<C ray emerges with certain deviation; If (r
2
=AC)=C or A=2C the emergent ray
just grazes the second surface; If (r
2
=AC)>C
or A>2C ray does not emerge out of the prism
due to TIR
Hence,
incident ray does not emerge out of the prism if A>2C for any value of angle of
incidence.
2
.
Spectrum
is a band of in an orderly arranged colours (or wavelengths)
It is produced by
dispersion.
⇒
it is the phenomenon of splitting of composite light (white light) into its constituent
colours (or wavelengths)
Pure spectrum is the one in which there is no overlapping of the colours (or wavelengths).
Spectrum is produced due to dispersion of light.
Dispersion takes place due to the variation of RI of the given material with wavelength of
light
. It is given by Cauchy’s formula,
RI=
2
B
A
n
λ
+
=
;
From violet to red wavelength of light ‘
λ
’ increases in the order of (VIBGYOR) hence in a given
medium RI decreases and velocity of light increases in the order of (VIBGYOR)
λ
v
<
λ
r
⇒
n
v
>n
r
⇒
V
v
<V
r
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3.
Pure Spectrum is produced by a spectrometer; it consists of
(a) Collimator: produce a parallel beam of light; consists of a thin slit and achromatic converging
lens with rack and pinion arrangements
(b) Prism table: It can be leveled and rotated about a vertical axis passing through its center
(c) Telescope: Converges the parallel beams of different colours deviated at different angles by the
prism in minimum deviation at different points on the screen. Converging lens is achromatic in
nature.
4
. Using spectrometer angle,
‘A’ of the prism, RI ‘n’ and dispersive power ‘
ϖ
’ of the material of
the prism can be determined. Note:
‘n’ and ‘
ϖ
’ are the constants of the material of the prism
Angular dispersion=
)A
n
(n
δ
δ
r
v
r
v

=

Mean deviation,
1)A
(n
δ
y
y

=
Dispersive power
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 Spring '10
 Bratton
 Angle of Incidence, Total internal reflection, Prism

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