Answer to Question #110673 in Optics for Abdullah ashraf

Question

Joe is told by his ophthalmologist that he requires glasses with a refractive power of −4.7 D to correct his vision. His previous prescription was −3.8 D.(a) Is Joe nearsighted or farsighted? (b) When Joe is not wearing his glasses, how far away can he see objects clearly? (c) When he wears his old prescription, how far away can he see clearly?

Answer 1

As per the given question,

Initially the power of lens=-3.8D

Finally the power of the glass =-4.7D

a)we know that, focal length =$-\dfrac{1}{P}=-\dfrac{100}{4.7}=-20.26cm$

-ive sign is describing the concave lens, which diverge the ray of light and due to which the image is getting shift on the ratina, Hence he have nearsightedness.

b) Wen joe is not wearning the glass, then

$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$

$\Rightarrow \dfrac{1}{u}=\dfrac{-1}{f}+\dfrac{1}{25}=\dfrac{-4.7}{100}+\dfrac{1}{25}=\dfrac{-7}{1000}$

$u=-\dfrac{1000}{7}=142.85cm$

c) If he wear old precision,

focal length =$\dfrac{100}{-3.8}=26.31cm$

$\dfrac{1}{u}=\dfrac{-3.8}{100}-\dfrac{1}{25}$

$\Rightarrow \dfrac{1}{u}=\dfrac{-1.8}{100}$

$u=\dfrac{100}{-1.8}=55.55 cm$