Given below are two statements : Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II : The refractive indices are different for different wavelengths in dispersive medium. In the light of the above statements, choose the correct answer from the options given below :

We need to evaluate two statements about the dispersion of white light through a prism.

Analysis of Statement I: "When white light passes through a prism, the red light bends lesser than yellow and violet."

This statement is true. When white light undergoes dispersion through a prism, different colours bend (refract) by different amounts. The degree of bending depends on the refractive index, which in turn depends on the wavelength. Red light has the longest wavelength in the visible spectrum and therefore has the smallest refractive index in a dispersive medium. Since a smaller refractive index means less bending (by Snell's law: $$n_1 \sin \theta_1 = n_2 \sin \theta_2$$), red light bends the least. The order of increasing bending is: red, orange, yellow, green, blue, indigo, violet (ROYGBIV).

Analysis of Statement II: "The refractive indices are different for different wavelengths in dispersive medium."

This statement is also true. This is the fundamental property that defines a dispersive medium. In such a medium, the refractive index is a function of wavelength, described by Cauchy's equation:

$$n(\lambda) = A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4} + \ldots$$

where $$A$$, $$B$$, $$C$$ are material-dependent constants. Since $$n$$ decreases with increasing $$\lambda$$, violet light (shortest wavelength) has the highest refractive index and red light (longest wavelength) has the lowest. This variation of refractive index with wavelength is the cause of dispersion.

Conclusion:

Both statements are true, and Statement II provides the underlying reason for the phenomenon described in Statement I.

The correct answer is Option (3): Both Statement I and Statement II are true.