People who do very detailed work close up, such as jewellers, often can see objects clearly at much closer distance than the normal 25 cm. a. What is the power in D of the eyes of a woman who can see an object clearly at a distance of only 8.5 cm

This question is incomplete, the complete question is;

People who do very detailed work close up, such as jewelers, often can see objects clearly at much closer distance than the normal 25 cm.

a) What is the power in D of the eyes of a woman who can see an object clearly at a distance of only 8.50 cm? (Assume the lens-to-retina distance is 2.00 cm.)

b) What is the size in mm of an image of a 8.00 mm object, such as lettering inside a ring, held at this distance? (Include the sign of the value in your answer.)  __ mm

Answer:

1) the power in D of the eyes of a woman is 61.7647 D

2) the size in mm of an image of a 8.00 mm object is -1.882 mm

Explanation:

Given the data in the question;

a) power in D of the eyes of woman who can see an object clearly at a distance of only 8.5 cm and the lens-to-retina distance is 2.00 cm,

so

u = 8.5 cm = ( 8.5 / 100 )m = 0.085 m

v = 2.00 cm = ( 2 / 100 )m =  0.02 m

Now, we know that power of lens p = 1 / u + 1 / v

so we substitute

p = ( 1 / 0.085 ) + ( 1 / 0.02 )

p = 11.7647 + 50

p = 61.7647 D

Therefore,  the power in D of the eyes of a woman is 61.7647 D

b) What is the size in mm of an image of a 8.00 mm object, such as lettering inside a ring, held at this distance? (Include the sign of the value in your answer.)

we know that;

m = -v / u

we substitute

m = -0.02 / 0.085

m = -0.2353

since H₀ = 8.0 mm

H[tex]_i[/tex] = m × H₀

H[tex]_i[/tex] = -0.2353 × 8.0

H[tex]_i[/tex] = -1.882 mm

the size in mm of an image of a 8.00 mm object is -1.882 mm

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