The left end of a long glass rod 6.20 cm in diameter has a convex hemispherical

Question

The left end of a long glass rod 6.20 cm in diameter has a convex hemispherical surface 3.10 cm in radius. The refractive index of the glass is 1.74. Determine the position of the image if an object is placed in air on the axis of the rod at the following distances to the left of the vertex of the curved end. a) infinitely far distance ____________ cm left or right of the vertex? b) 8.0 cm distance __________ cm left or right of the vertex c) 1.00 cm distance ______________ cm left or right of the vertex

Explanation / Answer

Using the formula:

1/u+2/V = |2-1|/r

1=1

2=1.74

r= 3.1

(a)

1/ + 1.74/V = |1.74-1|/3.1

1.74/V = |1.74-1|/3.1

V = 7.289 cm

Distance = 7.289 cm

right of the vertex

(b)

1/8 + 1.74/V = |1.74-1|/3.1

V=15.302 cm

Distance = 15.302 cm

right of the vertex

(c)

1/1 + 1.74/V = |1.74-1|/3.1

V=-2.286 cm

Distance = 2.286 cm

left of the vertex

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