A container contains water up to a height of 20 cm and there is a point source at the center of the bottom of the container. A rubber ring of radius r floats centrally on the water surface. The ceiling of the room is 2.0 m above the water surface.

(a) Find the radius of the shadow of the ring formed on the ceiling if r = 15 cm.


(b) Find the maximum value of r for which the shadow of the ring is formed on the ceiling. Refractive index of water = 4/3.


33.PNG


(i)Height of water container h= 20 cm


Ceiling of the room is 2.0 m above the water surface.


Radius of the rubber ring= r


Refractive index of water


From the figure we can say that;



By applying Snell’s law, we get;




From the figure, we get;



So,








So, the total radius of the shadow =


(b)For Maximum angle of refraction, angle of incidence should be equal to critical angle i.e.


Let R is the maximum radius.


Now,







.


1