An illuminated object is placed on the principal axis of a converging lens so that a real image is formed on the other side of the lens. If the object is shifted a little,

In an experiment to measure the speed of light by Fizeau's apparatus, the following data are used.

Distance between the mirrors$=12.0 \mathrm{km}$,

the number of teeth in the wheel$=180$.

Find the minimum angular speed of the wheel for which the image is not seen in ${10}^4 deg s^{-1}$.

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

Distance between the rotating and the fixed mirror$=16 \mathrm{m}$.

Distance between the lens and the rotating mirror$=6 \mathrm{m}$.

Distance between the source and the lens$=2 \mathrm{m}$.

When the mirror is rotated at a speed of $356$ revolutions per second, the image shifts by $0.7 \mathrm{mm}$. The speed of light is  $2.\mathrm{n}7\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$. Then find the value of integer $\mathrm{n}$.