Question

Assuming that Eq. 37-36 holds, find how fast you would have to go through a red light to have it appear green. Take 620 nm as the wavelength of red light and 540 nm as the wavelength of green light.

Short answer

The speed of observer for variation in colour of light from red to green is 0.13c.

Step-by-step solution

Identification of given data

The wavelength of red light is ${\mathrm{\lambda }}_{\mathrm{r}}=620\mathrm{nm}$

The wavelength of green light is ${\mathrm{\lambda }}_{\mathrm{g}}=540\mathrm{nm}$

The speed for the variation in the colour of light from red to green is found by using the formula for wavelength shift.

Determination of speed for change in red colour light into green light

The speed for variation in colour of light is given as:

$\mathrm{v}=\left(\frac{{\mathrm{\lambda }}_{\mathrm{r}}-{\mathrm{\lambda }}_{\mathrm{g}}}{{\mathrm{\lambda }}_{\mathrm{r}}}\right)\mathrm{c}$

Here, c is the speed of light.

Substitute all the values in the above equation.

$\begin{array}{rcl}\mathrm{v}& =& \left(\frac{620\mathrm{nm}-540\mathrm{nm}}{620\mathrm{nm}}\right)\mathrm{c}\\ & =& 0.13\mathrm{c}\end{array}$

Therefore, the speed of observer for variation in colour of light from red to green is 0.13c.