Question

if red and violet color are passing through same glass sheet simultaneously then relation between their velocity will be:
A. \[{V_r} = {V_v}\]
B. \[{V_r} < {V_v}\]
C. \[{V_r} > {V_v}\]
D. None of these

Answer 1

Hint: The velocities of the colored bands are dependent on their refractive index as well as their velocities. The relation between refractive index and velocity is that refractive index is inversely proportional to refractive index.

Complete step by step answer:
We know that a rainbow is made of 7 colors VIBGYOR violet, indigo, blue, green, yellow, orange, red. Among them the color which bends the least is red and the one that bends the most is violet. The refractive index of the above mentioned colors is as follows:
\[{n_v} > {n_i} > {n_b} > {n_g} > {n_y} > {n_o} > {n_r}\]
Where $n$ is the refractive index.
We also know that:
\[n = \dfrac{c}{v}\]
where $n$=refractive index, $c$= speed in vacuum (\[3 \times {10^8}m/s\]) and $v$ = velocity in another medium.
Hence by the above mentioned relation we can see that the refractive index is inversely proportional to velocity . Hence the order of velocities will be: \[{v_v} < {v_i} < {v_b} < {v_g} < {v_y} < {v_o} < {v_r}\]
looking at the above order of velocities we see that:
\[{v_v} < {v_r}\]

Hence the correct answer is option C.

Note: This question can also be solved keeping in mind the wavelengths of the band. The wavelength of violet is the least (it bends the most) and the wavelength of red is most( it bends the least).Also refractive index is inversely proportional to wavelength hence the refractive index of violet is most and that of red is least. Hence two points to remember are:
-Refractive index is inversely proportional to velocity
-The Reflective index is inversely proportional to wavelength.