Question

A container contains water upto a height of 20 cm and there is a point source at the centre of the bottom of the container. A rubber ring of radius r floats centrally on the water. 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.

Answer 1

given :

sin i/ sin r= 1/μ= 3/4

sin r= 4/5

again x/ 2= tanr from the figure

sinr = tanr /√(1+tan²r)=x/2/√(1-x²/4)

=x/(√(4+x²)=4/5

25x² = 16 (4+x²)

9x²=64

x= 8/3m

total radius of shadow= 8/3 +0.15 =2.81m

b) For maximum size of ring  :

i= critical angle =c

let R be maximum radius

sin C= Sin C/ sinR = R√/(20² + R²)= 3/4

since sin r=1

16 R²= 9R² +9x 400

7R²= 9x 400

R= 22. 67 cm

Answer 2

Here is your answer....