The left end of a long glass rod 6.00 c m in diameter has a convex hemispherical

Question

The left end of a long glass rod 6.00cm in diameter has a convex hemispherical surface 3.00cm in radius. The refractive index of the glass is 1.60. Distances are measured from the vertex of the hemispherical surface (to the right is positive for image distances).

1. Determine the position of the image if an object is placed in air on the axis of the rod at the infinitely far distance to the left of the vertex of the curved end.

2. Determine the position of the image if an object is placed in air on the axis of the rod at the distance of

12.00cm to the left of the vertex of the curved end.

3. Determine the position of the image if an object is placed in air on the axis of the rod at the distance of

2.00cm to the left of the vertex of the curved end.

Explanation / Answer

Apply n1/p + n2/q = (n2 - n1)/R

Part A)

p is infinite, so...

0 + 1.6/q = (1.6 - 1)/3

q = 8 cm

Part B)

1/12 + 1.6/q = (1.6 - 1)/3

q = 13.7 cm

Part C)

1/2 + 1.6/q = (1.6 - 1)/3

q = -5.33 cm

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