# Attack of the optics

Classical Mechanics Level 5

A point light source is moving with constant velocity $$v$$ inside a transparent thin spherical shell of radius $$R$$, which is filled with a transparent liquid. If at $$t=0$$ , light source is at the centre of the sphere, then at what time a thin dark ring will be visible for an observer outside the sphere. the refractive index of liquid with respect to that of shell is $$\sqrt{2}$$.

The time is of form $$\frac{R}{kv}$$, where k is a real number . Find k.

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