Focus at a single surface

Light travels left to right from air (n₁ = 1.0) into a semi-infinite medium (n₂ = 1.5) through a spherical surface. A point object is 0.30 m left of the vertex. The center of curvature is 0.10 m right of the vertex.

Find the signed image distance from the vertex, taking right as positive.

Organize the givens & assumptions

n₁ = 1.0, n₂ = 1.5
u = −0.30 m
R = +0.10 m

Paraxial refraction at a single interface; u = −0.30 m and R = +0.10 m in the stated Cartesian convention.

A $+0.90\ \mathrm m$
B $+0.18\ \mathrm m$
C $-0.90\ \mathrm m$
D $+0.60\ \mathrm m$

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