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.