A particular nearsighted patient can\'t see objects clearly when they are beyond

Question

A particular nearsighted patient can't see objects clearly when they are beyond 20 cm (the far point of the eye).

(a) What focal length should the prescribed contact lens have to correct this problem?
cm

(b) Find the power of the lens, in diopters. Neglect the distance between the eye and the corrective lens.
diopters

(a) What power lens would you prescribe for a patient with a far point of 36.5 cm? Neglect the eye–lens distance.
diopters

(b) Repeat, assuming an eye-corrective lens distance of 2.00 cm.
diopters

Explanation / Answer

a)

image distance v=20cm ( far point)

1/u+1/v=1/f

0+(1/-20cm)=1/f

===> f=-20cm

focal length of the presribed contact lens f=20cm

b)

power P=1/f

P=(1/-20cm)

P=-4 diapters (diverging lense)

c)

if the far pint is v=36.5 cm

1/u+1/v=1/f

1/u+1/v=1/f

0+1/(-36.5cm)=1/f

focal length f=-36.5 cm

power P=1/f

P=(1/-36.5cm)

P=-2.74 diapters (diverging lense)

d)

eye-correvtive lense distance is 2cm

part(a) ---> v=20-2 =18cm

then,

1/u+1/v=1/f

0+1/(-18cm) +1/v=1/f

===> f=-18cm

power P=1/(-18cm)=5.56 diapters

part(b) ---> v=36.5-2=34.5 cm

then,

1/u+1/v=1/f

0+1/(-34.5cm) +1/v=1/f

===> f=-34.5cm

power P=1/(-34.5cm)=2.9 diapters

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