Question

A cylindrical vessel, whose diameter and height both are equal to 30 cm, is placed on a horizontal surface and a small particle P is placed in it at a distance of 5.0 cm from the centre. An eye is placed at a position such that the edge of the bottom is just visible (see figure 18-E8). The particle P is in the plane of drawing. Up to what minimum height should water be poured in the vessel to make the particle P visible ?

Answer 1

Given  

Diameter of cylindrical vessel =30cm

r= 15cm

h= 30cm

sin i/ sinr = 3/4

sin i = 3/4 x √2

since r= 45 °

the point can be seen only when r= 45° at point of refraction

Let x be the distance of point from X

tan 45 = x+10/d

d= x+10

tan i = x/d

3/√23= d-10/d

since values of sin i =3/4√2 -> tan i = 3/√23

3/√23-1= - 10/d

d= √23 x10/ √23- 3=26.7cm

Answer 2

Your Answer Is Given Below:-

Diameter of cylindrical vessel =30cm

r= 15cm

h= 30cm

sin i/ sinr = 3/4

sin i = 3/4 x √2

since r= 45
°

the point can be seen only when r= 45° at point of refraction

Let x be the distance of point from X

tan 45 = x+10/d

d= x+10

tan i = x/d

3/√23= d-10/d

since values of sin i =3/4√2 -> tan i = 3/√23

3/√23-1= - 10/d

d= √23 x10/ √23- 3=26.7cm