Question

A person is myopic (Short Sighteded). Maximum focal length her/her eye can achieve is 8cm. The retina is at the distance of 10cm.
The doctor recommends a lens. A lens is worn at a distance of 1cm from the eye. What should be the power of the lens (in dioptres) that's prescribed by the doctor?

Answer 1

The farthest that person can see is 8 cm, that means that rays coming from an object 8 cm away from the eye can be focused properly, and beyond that rays can't be focused. When we wear spectacles, our eyes don't see the objects directly, instead they see only the image of the objects formed by the lenses of your spectacles. So wherever the image forms by spectacles, our eyes pretend that object to be at that point as if the object is shifted. So, in order to see some thing 10 cm away we should make sure that the image of object formed by spectacles should be 8 cm away so that eye could focus the rays coming from the image.

 

v

1

−

u

1

=

f

1

 

Object is 10 cm away from eye and so 9cm away from the lens of the spectacles, 

Image should be 8 cm from the eye and so 7 cm away from the lens of the spectacles. Taking the left side to the lens of spectacle to be positive: 

u=−9cm

 

v=

−7cm

Substituting this in the lens equation:

 

−7

1

−

−9

1

=

f

1

therefore f=-7×9/2 =-31•5 cm

Ans:--- the powder should be given 31•2cm.