If a glass prism is dipped in water, its dispersive power:
Here, denotes Angle of Prism.
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Snell's law of refraction states that the product n θ is the same on both sides of an interface. Here, θ is the angle between the light ray and the normal,, and n the index of refraction.
Since n air < n water < n glass , it follows that θ air > θ water > θ glass for comparable light rays. It follows that Δ θ water → glass < Δ θ air → glass .
Or, since the transition from glass to water involves a smaller change in refractive index n , it will also result in a smaller change in direction angle θ , leading to decreased dispersion.