Question 222: Wave Optics

Question

A galaxy is moving away from the earth at a speed of 286 kms
$$-$$1
. The shift in the wavelength of a redline at 630 nm is x $$	imes$$ 10
$$-$$10
m. The value of x, to the nearest integer, is ____________. [Take the value of speed of light c, as 3 $$	imes$$ 10
8
ms
$$-$$1
]

Accepted Answer

From Doppler effect, we know
$$\lambda ' = \lambda \left[ {1 + {v \over c}} ight]$$
here, $$v = 286 	imes {10^3}$$ m/s
$$c = 3 	imes {10^8}$$ m/s
$$ 	herefore $$ $$\lambda ' - \lambda  = {{\lambda v} \over c}$$
$$ = {{630 	imes {{10}^{ - 9}} 	imes 286 	imes {{10}^3}} \over {3 	imes {{10}^8}}}$$
= 6 $$	imes$$ 10
$$-$$10
m

Wave Optics

A galaxy is moving away from the earth at a speed of 286 kms $-1 . The shift in the wavelength of a redline at 630 nm is x \times 10 -10 m. The value of x, to the nearest integer, is ____________. [Take the value of speed of light c, as 3 \times 10 8 ms -$1 ]

Integer / Numeric Answer Type