A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance?

We know that speed of light in vacuum, c = 3 × 10⁸ m/s

Relation between speed & distance travelled

Distance travelled ‘x’ = speed × time taken ------- (1)

Here the value of time taken is given

t = 8 min 20 s = 500 s

So, x = s × t

x = c × t

Where c = speed of light

t = time taken

= 3 × 10⁸ ms^-1 × 500 m

= 1.5 × 10¹¹ m

So this is the distance between the sun and the earth.

We have to express the above distance value in terms of new units. In new units, the value of the speed of light is unity.

i.e, c = 1 unit

t = 500 s

Substituting the above values in equation (1)

Distance between sun & Earth x = c × t

= 1 unit × 500 s

= 500 new units

Distance between Sun & Earth = 500 new units