To fit a contact lens to a patient?s eye, a keratometer can be used to measure t

Question

To fit a contact lens to a patient?s eye, a keratometer can be used to measure the curvature of the front surface of the eye, the cornea. This instrument places an illuminated object of known size at a known distance p from the cornea. The cornea reflects some light from the object, forming an image of the object. The magnification M of the image is measured by using a small viewing telescope that allows comparison of the image formed by the cornea with a second calibrated image projected into the field of view by a prism arrangement. Determine the radius of curvature of the cornea for the case p = 29.0 cm and M = 0.0110. cm A convex spherical mirror has a focal length of magnitude 4.50 cm. (a) What is the location of an object for which the magnitude of the image distance is one-half the magnitude of the object distance? cm from the mirror (b) Find the magnification of the image. (c) State whether it is upright or inverted. upright inverted

Explanation / Answer

6.)

here

v = - 0.5* u

then by using the mirror formula

1 / f = 1 / v + 1 / u

1 / 4.50 = 1 / -0.5*u + 1 / -u

1 / 4.5 = (-2 -1 ) / u

u = -13.5 cm

the location of the object is -13.5 cm

b)

m = - v / u

m = - ( 0.5 * u / u )

m = 0.5

so the magnification of the mirror is 0.5

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