The left end of a long glass rod 8.00 c m in diameter and with an index of refra

Question

The left end of a long glass rod 8.00cm   in diameter and with an index of refraction of 1.60 is ground and polished to a convex hemispherical surface with a radius of 4.00cm. An object in the form of an arrow 1.10mm  tall, at right angles to the axis of the rod, is located on the axis 22.0cm  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. answer is s'= 15.3 cm

Find the height of the image formed by paraxial rays incident on the convex surface. absolute value y'=______mm

Explanation / Answer

1)

1/22 +1.6/s' = (1.6-1)/4

0.045 + 1.6/s' = 0.15

1.6/s' = 0.1

s' = 15.238 cm

2)

Magntifcation = image height/object height

= image distance/object diatance

= s'/s

==> y'/1.1 = 15.238/22

y' = 0.762 mm

or =0.762 mm

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