Refraction of Light Through Prism
Ordinary white light, as we know, is a superimposition of waves having wavelength throughout the visible spectrum
Prism is that optical instrument which splits this white light into its constituent wavelengths
A prism dispersing white light into its composite wavelengths or colours
This breaking up of white light inside a prism happens through refraction at the prism-air interface
Let us now understand some mathematical relations incorporating Refraction of light through a prism
We consider the principal section of a prism,
A
B
C
Let two normals
N
1
M
and
N
2
M
be incident on the interfaces
A
B
and
A
C
respectively
Let a ray
P
Q
be incident on
A
B
making an incident angle
i
As the ray is travelling from rarer to denser medium; it bends towards the normal
Then it refracts at
A
C
and bends away from the normal (denser to rarer) forming the emergent ray
This emergent ray forms an angle
e
with the normal at
A
C
known as the angle of emergence
The angles of refraction are
r
1
and
r
2
respectively
Now if the emergent ray is extended backwards to
O
, then we get the angle of deviation, denoted by
δ
δ
tells, to what extent the ray PQ had bent from its original path PQOR to OS, owing to refraction by the prism
Now consider
△
O
Q
T
Let,
∠
O
Q
T
=
α
,
∠
O
T
Q
=
β
∴
δ
=
α
+
β
(Sum of Int angles=Ext angle)
Now from the diagram, we can write the interior angles as
α
+
r
1
=
i
∴
α
=
i
−
r
1
Similarly
β
=
e
−
r
2
Now simplifying the equation
δ
=
α
+
β
we get
δ
=
i
−
r
1
+
e
−
r
2
→
δ
=
i
+
e
−
(
r
1
+
r
2
)
Now let us consider quadrilateral
A
Q
M
T
∠
A
Q
M
+
∠
A
T
M
=
1
8
0
0
(MQ and MT are normals)
So, we can say quadrilateral
A
Q
M
T
is cyclic
∴
∠
A
+
∠
M
=
1
8
0
0
→
Eqn 1
In
△
M
Q
T
∠
r
1
+
∠
r
2
+
∠
M
=
1
8
0
→
Eqn 2
From Eqn 1 and 2 we get,
∠
r
1
+
∠
r
2
+
∠
M
=
∠
M
+
∠
A
∴
∠
r
1
+
∠
r
2
=
∠
A
As
A
=
r
1
+
r
2
and
δ
=
i
+
e
−
(
r
1
+
r
2
)
∴
δ
=
i
+
e
−
A
→
δ
+
A
=
i
+
e
Thus we get a relation between the angle of deviation
δ
, the angle of prism
A
, the angle of incidence
i
and the angle of emergence
e
Revision
The relation between
δ
and
A
is
δ
+
A
=
i
+
e
also
A
can be written as
A
=
r
1
+
r
2
The relation
δ
+
A
=
i
+
e
relates between the angle of deviation
δ
, the angle of prism
A
, the angle of incidence
i
and the angle of emergence
e
The End