The left end of a long glass rod 6.64cm in diameter and with an index of refract

Question

The left end of a long glass rod 6.64cm in diameter and with an index of refraction of 1.485 is ground and polished to a convex hemispherical surface with a radius of 3.32cm . An object in the form of an arrow 3.78mm tall, at right angles to the axis of the rod, is located on the axis 21.44cm to the left of the vertex of the convex surface.

Find the position of the image of the arrow formed by paraxial rays incident on the convex surface.

Find the height of the image formed by paraxial rays incident on the convex surface.

Explanation / Answer

image object relation of spherical refracting surface is

n_air / D_obj + n_glass / D_img = (n_glass - n_air) / Radius

1 / 21.44 + 1.485 / D_img = (1.485 - 1) / 3.32

D_img = 14.9332 cm

position of the image of the arrow = 14.9332 cm

magnification = n_air * D_img / n_glass * D_obj

magnification = 1 * 14.9332 / 1.485 * 21.44

magnification = 0.469

height of image = magnification * height of object

height = 0.469 * 3.78

height of image = 1.77282 mm

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