The correct option is Both A and R are true and R is the correct explanation of A.
Explanation
The phenomenon described is dispersion, where white light splits into its constituent spectral colors upon passing through a prism. The extent to which each color bends (deviates) depends on the refractive index of the glass for that specific wavelength of light.
Statement-wise Analysis
- Assertion (A): Correct. When white light passes through a glass prism, it disperses into the spectrum VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red). The angle of deviation is the angle between the incident ray and the emergent ray. Red light has the longest wavelength ($\lambda$) in the visible spectrum and undergoes the least deviation, while violet light has the shortest wavelength and undergoes the maximum deviation.
- Reason (R): Correct. The refractive index ($n$) of a medium is defined as the ratio of the speed of light in a vacuum ($c$) to the speed of light in that medium ($v$), given by $n = \frac{c}{v}$. According to Cauchy’s relation, the refractive index is inversely proportional to the wavelength ($n \propto \frac{1}{\lambda}$). Since red light has the longest wavelength, the glass has the lowest refractive index for red light. Consequently, the speed of red light in glass is the maximum among all visible colors ($v = \frac{c}{n}$).
- Justification for
Both A and R are true and R is the correct explanation of A
: The angle of deviation ($\delta$) is directly related to the refractive index ($n$). For a thin prism, $\delta \approx A(n-1)$. Since the speed of red light is maximum, its refractive index ($n$) is minimum. A minimum refractive index results in the minimum angle of deviation. Therefore, the fact that red light travels fastest in glass (Reason) is the physical cause for it deviating the least (Assertion).
Key Takeaway
Relationship between Wavelength, Speed, and Deviation:
$\text{Wavelength } (\lambda) \uparrow \Rightarrow \text{Speed in medium } (v) \uparrow \Rightarrow \text{Refractive Index } (n) \downarrow \Rightarrow \text{Angle of Deviation } (\delta) \downarrow$.
Red light follows this sequence (max $\lambda$, max $v$, min $n$, min $\delta$).