Q:To fit a contact lens to a patient\'s eye,a keratometer can be used to measure

Question

Q:To fit a contact lens to a patient's eye,a keratometer can be used to measure thecurvature of the cornea-the front surface of the eye. Thisinstrument places an illuminated object of known size at a knowndistance p from the cornea, which then reflectssome light from the object, forming an image of it. Themagnification Mof the image is measured by using asmall viewing telescope that allows a comparison of the imageformed by the cornea with a second calibrated image projected intothe field of view by a prism arrangement. Determine the radius ofcurvature of the corneawhen p = 32.0 cmand M = 0.0170.
mm
mm mm

Explanation / Answer

given distance of object from the cornea P = 32cm magnification M = 0.0170 we have the mirror equation as    1/p + 1/q = 1/f but focal length f = R/2     so 1/p + 1/q = 2/R    the magnification is M = -q/p                          or q = -Mp                                   = -(0.0170)(32cm)                                    = -0.544cm so      1/p + 1/q = 2/R or      R = 2pq/p+q           =2*32*-0.544 / 32-0.544           =-1.106cm           =-11.06mm as R is -ve , so the surface of cornea isconvex        

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