At a spherical refractive interface, an object in medium μ₁=1.3 is 13 cm from the surface and forms a real image in medium μ₂=1.4 that is twice in size. The radius of curvature is:
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At a spherical refractive interface, an object in medium μ₁=1.3 is 13 cm from the surface and forms a real image in medium μ₂=1.4 that is twice in size. The radius of curvature is:

G1 Physics · Accepted Answer

For re f r a c t i o n fraction f r a c t i o n at a spherical surface, transverse magnification m=(μ₁v)/(μ₂u). With m=-2 and u=-13 cm, v=+28 cm. Then μ₂/v-μ₁/u=(μ₂-μ₁)/R gives 1.4/28-1.3/(-13)=0.1/R. Thus 0.05+0.10=0.1/R, so R=2/3 cm.