A spider is hanging by means of its own silk thread directly above a transparent fixed sphere of r = 20cm .... the refractive index of material of sphere is root(2).... and height of the spider is 2r = 40cm .... an insect initially sitting at the bottom directly below the spider starts crawling along vertical circular path with constant speed pi/4 cm/s.. for how long will the insct be invisible to the spider. Assume that it crawls once around the circle .Solution) Spider is able to see only half of the sphere which is topmost hemispherical surface. when insct enters in bottom hemispherical surface it becomes invisible for the spider. a/c question insct is travelling vertical circular path it travels pi/4cm in 1sec.then it will travel 2pi r dist i.e. 40picm in 160sec. hence it will travel pi r i.e20pi (half circle) in 80s.