The fundamental difference between the angle of incidence and the angle of refraction at each refracting surface of a prism is what causes light to change direction as it passes through the prism. This phenomenon of bending light leads to the overall deviation of the light ray from its original path.
Understanding Refraction at Prism Surfaces
A prism typically has two refracting surfaces where light enters and exits. At each of these surfaces, light passes from one medium (like air) to another (like glass) or vice-versa, causing it to bend due to the change in speed.
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First Surface (Light Entering):
- The angle at which the incoming light ray strikes the surface is the angle of incidence (i₁).
- The angle between the refracted ray inside the prism and the normal to the surface is the angle of refraction (r₁).
- When light enters a denser medium (like glass from air), it bends towards the normal. This means the angle of incidence (i₁) is typically greater than the angle of refraction (r₁). The difference (i₁ - r₁) represents the change in direction at this surface.
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Second Surface (Light Exiting):
- The angle at which the light ray inside the prism strikes the second surface is the angle of incidence (r₂) (with respect to the normal at this surface).
- The angle at which the light ray exits the prism into the surrounding medium is the angle of refraction, often called the angle of emergence (e).
- When light exits a denser medium (like glass into air), it bends away from the normal. This means the angle of emergence (e) is typically greater than the angle of incidence inside the prism (r₂). The difference (e - r₂) represents the change in direction at this surface.
The Bending Effect and the Angle of Deviation
As highlighted by the provided information: "If you compare the angle of incidence and the angle of refraction at each refracting surface of the prism, you will find the peculiar shape of the prism makes the emergent ray bend at an angle to the direction of the incident ray."
This statement precisely describes the consequence of the difference between these angles at each surface. Because the angle of incidence and the angle of refraction are different at both the entry and exit points, the light ray's direction is altered. The unique angles and geometry of the prism ensure that these individual bendings typically combine to deflect the light ray significantly from its original path.
The overall change in direction of the light ray after passing through the prism is quantified by the angle of deviation. As the reference explains: "This angle is called the angle of deviation. In this case ∠D is the angle of deviation."
Therefore, while the exact numerical difference (i₁ - r₁) at the first surface or (e - r₂) at the second surface depends on factors like the prism's material, the angle of incidence, and the prism's apex angle, the existence of these differences at each refracting surface is the fundamental reason light is bent by a prism, resulting in the observable angle of deviation. The deviation ∠D represents the net effect of the bending caused by the difference in angles at both surfaces.
