The correct answer is Option A: Both Statement I and Statement II are true.

Explanation:

Statement I discusses the dispersion of white light through a prism, which is a phenomenon where white light splits into its component colors when passed through a prism. This happens because different colors (or wavelengths) of light bend (refract) by different amounts upon passing through a prism. Red light bends the least while violet bends the most, with yellow falling somewhere in between. This is why the statement, "When the white light passed through a prism, the red light bends lesser than yellow and violet," is true.

Statement II addresses the underlying cause of the dispersion of light, which is that the refractive index of a medium varies with wavelength (or color) of light. This property of the medium is known as dispersion. A refractive index determines how much light bends when entering a medium. Since the refractive index varies with the wavelength, different colors of light bend by different amounts when they pass through a dispersive medium like a glass prism. This is why violet light bends more than red light - because the refractive index for violet light is higher than that for red light in glass. Therefore, the statement, "The refractive indices are different for different wavelengths in dispersive medium," is also true.

Thus, both statements I and II accurately describe the principles behind the phenomenon of light dispersion through a prism, making Option A the correct choice.