The left end of a long glass rod 6.95cm in diameter and with an index of refract

Question

The left end of a long glass rod 6.95cm in diameter and with an index of refraction of 1.586 is ground and polished to a convex hemispherical surface with a radius of 3.475cm . An object in the form of an arrow 3.13mm tall, at right angles to the axis of the rod, is located on the axis 22.5cm 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

na/s + nb/s' = (nb-na)/R

(1/22.5) + (1.586/s') = (1.586-1)/3.475)

s' = 12.77 cm <------answer

hi ho = -si/s

hi = (3.13*12.77)/22.5) = 1.776 mm <--------answer

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