Question

A spaceship moves with speed V relative to an observer O, on a straight line

which passes very near the observer. A source on the spaceship emits light of

wavelength kO ¼ 500 nm in the frame of reference of the spaceship. For what range

of the spaceship’s speed will the light be visible to the observer? The wavelengths of

visible light stretches from kA ¼ 400 nm to kB ¼ 700 nm, approximately.

Answer 1

$v_A=c\sqrt{1-\frac{k_A^2}{k_O^2}}=0.60c,$

$v_B=c\sqrt{\frac{k_B^2}{k_O^2}-1}=0.98c.$