Optometrists use an instrument called a keratometer to measure the curvature of

Question

Optometrists use an instrument called a keratometer to measure the curvature of the cornea. To apply this technique, an object of height 1.70 cm is held 3.00 cm from a patient's cornea, and its reflected image is measured. If the reflected image is upright and has a height of 0.185 cm, what type of mirror is the cornea? What is the magnification of the mirror formed by the cornea? What is the focal length of the mirror? Remember the sign convention for mirrors! Finally, what is the magnitude of the radius of curvature of the cornea?

Explanation / Answer

The cornea is convex because upright and diminished image is possible only for concex mirrors.

Magnification M = height of image/height of the object = 0.185/1.70 = 0.109

Given, object distance Do = 3cm

Now, Di/Do = -Hi/Ho => Di = (-0.185/1.70) x 3 = -0.326cm

So we have using mirror equation:

1/f = 1/Do + 1/Di => f = -0.366cm

Magnitude of R:

R = 2f = 0.731cm

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