How does the path at which a ray of light strikes a prism compare to the path after emergence from the other side?

This is the reason why the path at which a ray of light strikes a prism is different to the path after emergence from the other side. There is a refraction of light ray when the light passes from one medium to another at angle. Its speed changes. The bend is in one direction if the material it enters is denser, and other direction if less dense. The amount of bending is different because of different wavelengths.