A diffraction grating contains lots of equally spaced slits very close together hence splits and diffracts light into several beams travelling in different directions. You will need to know how to derive d sin(θ) = n λ using trigonometry.
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From a less optically dense material to a more optically dense material, waves refract towards the normal. From a more optically dense material to a less optically dense material, waves refract away from the normal. The higher a material's optical density, the higher refractive index.
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