Question 15 Marks
In an experiment with Foucault's apparatus, the various distances used are as follows:
Distance between the rotating and the fixed mirror $= 16m$
Distance between the lens and the rotating mirror $= 6m$
Distance between the source and the lens $= 2m$
When the mirror is rotated at a speed of 356 revolutions per second, the image shifts by 0.7mm. Calculate the speed of light from these data.
Distance between the rotating and the fixed mirror $= 16m$
Distance between the lens and the rotating mirror $= 6m$
Distance between the source and the lens $= 2m$
When the mirror is rotated at a speed of 356 revolutions per second, the image shifts by 0.7mm. Calculate the speed of light from these data.
Answer
View full question & answer→In the given Focault experiment, R = Distance between fixed and rotating mirror = 16m$\omega$ = Angular speed $= 356\text{rev/ s} = 356 × 2\pi \text{ rad/ sec}$
$b =$ Distance between lens and rotating mirror = 6m
$a =$ Distance between source and lens = 2m
$s =$ shift in image $= 0.7cm = 0.7 \times 10^{-3}m$
So, speed of light is given by,
$\text{C}=\frac{4\text{R}^2\omega\text{a}}{\text{s}(\text{R}+\text{b})}=\frac{4\times16^2\times356\times2\pi\times2}{0.7\times10^{-3}(16+6)}=2.975\times10^8\text{m/s}$
$b =$ Distance between lens and rotating mirror = 6m
$a =$ Distance between source and lens = 2m
$s =$ shift in image $= 0.7cm = 0.7 \times 10^{-3}m$
So, speed of light is given by,
$\text{C}=\frac{4\text{R}^2\omega\text{a}}{\text{s}(\text{R}+\text{b})}=\frac{4\times16^2\times356\times2\pi\times2}{0.7\times10^{-3}(16+6)}=2.975\times10^8\text{m/s}$