1. The left end of a long glass rod 8.00 cm in diameter, with an index of refraction of 1.60, is ground and polished to a concave hemispherical surface with a radius of 4.00 cm. An object in the form of an arrow 1.5 mm tall, at right angles to the axis of the rod, is located on the axis 24 cm to the left of the vertex of the concave surface.
a) Is the radius of curvature of the hemispherical surface positive or negative?
b) Find the position of the image of the arrow formed by the paraxial rays incident on the concave surface.
c) Find the height of the image of the arrow formed by the paraxial rays incident on the concave surface.
d) Is the image erect or inverted?
e) Find the position of the image if the glass rod and the arrow object were immersed into water with index of refraction 1.33.
f) Find position in air of image if the left end of the rod were polished to a plane surface.