People who do very detailed work close up, such as jewellers, often can see objects clearly at much closer distance than the normal 25.0 cm. What is the power of the eyes of a woman who can see an object clearly at a distance of only 9.75 cm? Assume a distance from the eye lens to the retina of 2.00 cm. Number diopters What is the size of the image of a 2.00 mm object, such as lettering inside a ring, held at this distance? Enter your answer as a positive number if the image is upright, and negative if it is inverted. Number mmWhat would the size of the image be if the object were held at the normal 25.0 cm? Number mm

a)    P = 60.26 diopter ,  b)   h´ = -0.4 mm ,  c)   h´ = -0.16 mm

Explanation:

a)  For this exercise we use the equation for thin lenses

               1 / f = 1 / p + 1 / q

where f is the focal length, p the distance to the object and q the distance to the image

in this case q is the distance from the lens to the retina q = 2.00 cm

the distance p is the distance from the object to the lens p = 9.75 cm

               1 / f = 1 / 9.75 + 1/2

               1 / f = 0.6026 cm⁻¹

power is the inverse of the focal length in meters

              P = 1 / f [m]

              P = 0.6026 102

              P = 60.26 diopter

b)  the size of the image

             m = - p / q

             m = - 2 / 9.75

             m = -0.2 X

if we assume that the object is right

            m = h´ / h

            h´ = m h

            h´ = -0.2 2

            h´ = -0.4 mm

if the height of the object h is straight the image and inverted

c) if the object were at p = 25.0 cm

           m = - 2/25

           m = -0.08

             h´ = -0.08 2

             h´ = -0.16 mm

the image would be much smaller