When a patient is being fitted with contact lenses, the curvature of the patient

Question

When a patient is being fitted with contact lenses, the curvature of the patient's cornea is measured with an instrument known as a keratometer. A lighted object is held near the eye, and the keratometer measures the magnification of the image formed by reflection from the front of the cornea. If an object is held 11.5cm in front of a patient's eye, and the ratio of the height of the reflected image to that of the object is 0.025, what is the radius of curvature of the patient's cornea? ______mm

Explanation / Answer

magnification m = v/u = 0.025

or v = 0.025 u

here u = 11.5 cm

so v= 11.5 *0.025 = 0.2875 cm

now 1/f = 1/u +1/v

f = uv/u+v

f = 0.2875* 11.5/(11.5+0.2875)

f = 0.2804

as f= R/2

R = 2f = 2*0.2804 =0.56 cm

= 5.6 mm

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