Q. How fast a person should drive his car so that the red signal of light appears green? (Wavelength for red colour $= 6200\mathring{\mathrm{A}}$ and wavelength for green colour $= 5400\mathring{\mathrm{A}}$)
A) $1.5 \times 10^{8}m/s$
B) $7 \times 10^{7}m/s$
C) $3.9 \times 10^{7}m/s$
D) $2 \times 10^{8}m/s$
Explanation
(c) Doppler shift (Source moving towards observer)
$\lambda^{'} = \lambda\left( 1 - \frac{V}{C} \right)$
$5400\mathring{\mathrm{A}} = 6200\mathring{\mathrm{A}}\left( 1 - \frac{V}{C} \right)$
$V = \left\lbrack 1 - \frac{54}{62} \right\rbrack C = 3.9 \times 10^{7}approx$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.