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Dispersion of White light analysis , Normal prism and thin prism

From Online Sciences - October 22, 2017

When a light ray falls on a triangular prism in a certain position , it emerges from the prism , dispersed into a rainbow , There are two types of triangular prism which are normal prism and thin prism , But the rectangular glass does not disperse the light because it acts as two similar reversed prisms , one cancel the dispersion of the other .

The normal prism

If a light ray falls on the face of the prism , it refracts inside the prism until it falls on the second face and emerges from the prism , The light ray refracts twice , The light ray deviates from its path by a certain angle , which is called angle of deviation ( ) .

Angle of deviation ( ) is the angle subtended by the direction of the extension of the incident ray and the emerging ray in a triangular prism .

Apex angle ( A ) is the confined angle between the two sides of prism , one of them , the light ray falls on it and the other , the light ray emerges from it .

When the angle of deviation of a triangular prism = 35 , this means that the angle subtended by the directions of the extension of the incident ray and the emerging ray = 35 .

Deduction of the laws of a triangular prism

The apex angle of the prism ( A ) :

A = 1 + 2

Where :1 is the angle of refraction at the first surface and 2 is the angle of incidence at the second surface .

The angle of deviation ( ) :

= ( 11) + ( 22 )

Where : 1 is the angle of incidence at the first surface and 2 is the angle of emergence .

= ( 1 + 2 )A

Tracing the path of the light ray in the triangular prism :

First : The angle of incidence on the first surface ( 1 )

When 1 > 0 , The light ray refracts inside the prism and falls on the other surface .

sin 1 = sin 1 / n , A = 1 +2

When 1 = 0 , The light ray passes without any refraction .

1 = 1 = 0 , A = 2

Second : The angle of incidence on the second surface ( 2 ) :

When 2 > c ( the critical angle of prism ) , The light ray reflects totally inside the prism .

Angle of incidence = Angle of reflection .

When 2 < c , The light ray refracts and emerges from the prism near to the separating surface ( away from the normal ) .

sin 2 = n sin 2

Third : The angle of emergence ( 2 ) .

When 2 = 90 , The light ray emerges tangent to the separating surface .

2 = c , A =1 + c

When 2 = 0 , The light ray emerges normal to the opposite surface of the prism .

2 = 2 = 0 , A =1

Factors affect the angle of deviation in the triangular prism

According to the relation := ( 1 + 2 )A

The angle of deviation in a prism of apex ( A ) depends on the angle of incidence (1 ) only .

The angle of deviation decreases as the angle of incidence ( 1 ) increases until it reaches its minimum value ( o ) and then increases again by increasing ( 1 ) .

The value of ( o ) is called the minimum angle of deviation .

Conditions of minimum angle of deviation :

The minimum angle of deviation ( o ) is the least angle of deviation of the light ray in the prism at which the angle of incidence equals the angle of emergence .

When the minimum angle of deviation of the light in a triangular prism = 30 , this means that it is the least angle of deviation of the light ray in the prism at which the angle of incidence equals the angle of emergence = 30 .

Deduction of prisms refractive index set at the minimum angle of deviation :

When the prism is in the position of minimum deviation :

1 = 2 = o ,1 =2 = o

o = 2oAo = ( o + A ) / 2

A = 2 oo = A / 2

n = sin o / sin on = sin ( (o + A ) / 2 )sin ( A / 2 )

The apex angle of the prism is constant , Accordingly , as the refractive index of the prism differs for each colour , the minimum angle of deviation also differs for each colour .

When o increases , n increases also and vice versa , The refractive index ( n ) depends on the wavelength n 1 /o depends on the wavelength .

Dispersion of the white light by a triangular prism :

The thin prism

Deviation angle

Angular dispersion

Dispersive power

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