The left end of a long glass rod 8.00 cm in diameter, with an index of refraction of 1.56, is ground and polished to a convex hemispherical surface with a radius of 4.00 cm. An object in the form of an arrow 1.51 mm tall, at right angles to the axis of the rod, is located on the axis 23.0 cm to the left of the vertex of the convex surface.
a. Find the position and height of the image of the arrow formed by paraxial rays incident on the convex surface.
b. Is the image erect or inverted?

The image mentioned is in the attachment

a) P = 2450 Pa;

b) P = 2940 Pa;

c) F = 4.9 N

Explanation:

a) Pressure is a force applied to a surface of an object or fluid per unit area.

The image shows a block applying pressure on the large side of the piston. The force applied is due to gravitation, so:

P =

P =

P =

P = 2450 Pa

The pressure generated by the block is P = 2450 Pa.

b) A static liquid can also exert pressure and can be calculated as:

ρ.g.h

where

ρ is the density of the fluid

h is the depth of the fluid

g is acceleration of gravity

600.9.8.0.5

2940 Pa

The pressure in the fluid at 50 cm deep is 2940 Pa.

c) For the system to be in equilibrium both pressures, pressure on the left side and pressure on the right side, have to be the same:

=

F =

Adjusting the units, = 0.002 m².

F =

F = 4.9 N

The force necessary to be equilibrium is F = 4.9 N.