In an experiment with Foucault's apparatus, the various distances used are as follows:

Distance between the rotating and the fixed mirror = 16 m

Distance between the lens and the rotating mirror = 6 m,

Distance between the source and the lens = 2 m.

When the mirror is rotated at a speed of 356 revolutions per second, the image shifts by 0.7 mm. Calculate the speed of light from these data.

#### Solution

Distance between the rotating and the fixed mirror (*R*) = 16 m

Distance between the lens and the rotating mirror (*b*) = 6 m

Distance between the source and the lens (*a*) = 2 m

Mirror is rotated at a speed of 356 revolutions per second

⇒ *ω *= 356 rev/s= 356 × 2 π rad/sec

Shift in the image (*s*) = 0.7 m = 0.7 × 10^{3} m

In Foucault experiment, speed of light is given by \[c = 4 R^2 \frac{wa}{s(R + b)}\]

\[= \frac{4 \times (16 )^2 \times 356 \times 2\pi \times 2}{(0 . 7) \times {10}^{- 3} (16 + 6)}\]

= 2.975 × 10^{8} m/s

Therefore, the required speed of light is 2.975 × 10^{8} m/s.