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A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit, if light takes $8 \mathrm{~min}$ and $20 \mathrm{sec}$ to cover this distance?
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Velocity of light $\mathrm{c}=1$ new unit of length $\mathrm{s}^{-1}$
Time taken by light of Sun to reach the Earth $=t=8 \min 20 \mathrm{~s}=8 \times 60+20=500 \mathrm{~s}$
$\therefore \quad$ Distance between the Sun and Earth,
$x=c \times t=1$ new unit of length $\mathrm{s}^{-1} \times 500 \mathrm{~s}$
$=500$ new units of length.
Time taken by light of Sun to reach the Earth $=t=8 \min 20 \mathrm{~s}=8 \times 60+20=500 \mathrm{~s}$
$\therefore \quad$ Distance between the Sun and Earth,
$x=c \times t=1$ new unit of length $\mathrm{s}^{-1} \times 500 \mathrm{~s}$
$=500$ new units of length.
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