Question

A nearsighted person wants to see an apple that is 7 meters away but can only clearly see objects that are at most 62 cm away from her eyes. Eyeglasses made of diverging corrective lenses can help her to see the apple clearly. If her glasses are 2.5 cm in front of her eyes, what should be the power of these corrective lenses to allow her to see the apple?

Answer 1

Answer:

The power of the corrective lenses is 3.162 D.

Explanation:

Given that,

Object distance = 70 cm

Image distance = 62 cm

Distance between eyes and glasses = 2.5 cm

Eyeglasses made of diverging corrective lenses can help her to see the apple clearly

So now ,

Object distance from glass =70-2.5 = 67.5 cm

Image distance from glass = 62-2.5 = 59.5 cm

We need to calculate the focal length

Using formula for focal length

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

$\dfrac{1}{f}=-\dfrac{1}{59.5}-\dfrac{1}{67.5}$

$\dfrac{1}{f}=-\dfrac{508}{16065}\ cm$

We need to calculate the power of lens

Using formula of power

$P=\dfrac{100}{f}$

$P=-\dfrac{508}{16065}\times100$

$P=-3.162 \ D$

Negative sign shows the lens is diverging.

Hence, The power of the corrective lenses is 3.162 D.