Attack of the optics

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.