Question

An object 3.112 cm high is held 4.00 cm from a person’s cornea, and its reflected image is measured to be 1.989 cm high.

(a) What is the magnification? _____

(b) Where is the image? ______ cm

(c) Find the radius of curvature of the convex mirror formed by the cornea. ______ cm

answer to the nearest 3 decimal places

Answer 1

a)

$\Gamma=\frac Hh=\frac{1.989}{3.112}=0.639,$

b)

$d=f\Gamma=4\cdot 0.639=2.556~cm,$

c)

$\frac 1F=\frac 2R=\frac 1f+\frac 1d=\frac1f+\frac{1}{f\Gamma}=\frac{\Gamma+1}{f\Gamma}\implies$ $R=\frac{2f\Gamma}{\Gamma+1}=\frac{2\cdot 4\cdot 0.639}{0.639+1}=3.119~cm.$