Question

An observer is approaching with velocity v towards a light source. If the velocity of light is c, then velocity of light with respect to observer will be
A. $c-v$
B. $c$
C. $c+v$
D. $\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}$

Answer 1

Hint: You could read the question carefully and thus grasp the situation well. Thereby, you will understand that the observer and light is traveling in opposite directions. Now, you could find the relative value assigning the directions accordingly. Then, think of the known facts on the speed of light and hence find the answer.

Complete answer:
In the question, we are given a situation in which an observer is moving with some velocity v towards a light source. We are given the velocity of light as c and we are supposed to find the velocity of light with respect to the observer.
If you’re familiar with special relativity we know that c is the upper speed limit for any conventional matter, any information or energy traveling through the coordinate space.
So, in the given situation, the speed of the observer will be much less than the speed of light.
The speed of light with respect to the observer moving in opposite direction $=c-\left( -v \right)=c+v$
But,$c\gg v$, so v can be taken as a negligible value. So,
Speed of light with respect to the observer will also be c. Hence, option B is the correct answer.

Note: Here, c is the speed of light in vacuum is a universal physical constant and is known to have the value given by,
$c=3\times {{10}^{8}}m/s$
This value isn’t just confined to speed of light but is also known to be the speed of gravitational waves, EM radiations, mass-less particles in vacuum and other field perturbations.