Question 115: Wave Optics

Question

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $$\mathop A\limits^o $$ is observed at 5896 $$\mathop A\limits^o $$ ?

Accepted Answer

$$f = {f_0}\sqrt {{{1 + \beta } \over {1 - \beta }}} $$
$$\beta  = {v \over c}$$
$${f \over {{f_0}}} = \sqrt {{{1 + \beta } \over {1 - \beta }}} $$
$${\left( {1 + {{\Delta f} \over {{f_0}}}} ight)^2} = (1 + \beta ){(1 - \beta )^{ - 1}}$$
$$\beta$$ is small compared to 1
$$\left( {1 + {{2\Delta f} \over {{f_0}}}} ight) = (1 + 2\beta )$$
$$\beta  = {{\Delta f} \over {{f_0}}} = {v \over c}$$
$$v = 6 	imes {c \over {5890}} = 305.6$$ km/s

Answer

306 km/sec

Answer

322 km/sec

Answer

296 km/sec

Answer

336 km/sec

Wave Optics

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $\mathop A\limits^o is observed at 5896 \mathop A\limits^o $ ?

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