Question

What is the ratio of velocities of light rays of wavelengths $4000°\mathrm{A}$ and $8000°\mathrm{A}$ in vacuum?

• A. $1:2$
• B. $1:1$
• C. $2:1$
• D. cannot be determined

Answer 1

The correct option is B

$1:1$

Step 1: Given Data:

Wavelengths $\left({\lambda }_1={4000}^{\circ }A,{\lambda }_2={8000}^{\circ }A\right)$ are given.

Step 2: Concept:

1. Light is an electromagnetic wave, which has a constant speed (velocity) when traveling in space (vacuum).
2. The value of this speed is approximately $c=3\times {10}^8\mathrm{m}/\mathrm{s}$, irrespective of the wavelength of the wave.

Step 3: Finding the ratio of velocities:

$\begin{array}{rcl}\frac{velocityfor4000°Alight}{velocityfor8000°Alight}& =& \frac{c}{c}\\ & =& \frac{3\times {10}^{8}m/s}{3\times {10}^{8}m/s}\\ & =& \frac{1}{1}\end{array}$

Hence, the ratio of the two velocities will be $1:1$ and option (B) is the correct option.