Question

A certain child's near point is 12.5 cm; her far point (with eyes relaxed) is 117 cm. Each eye lens is 2.00 cm from the retina. (a) Between what limits, measured in diopters, does the power of this lens–cornea combination vary? lower bound diopters upper bound diopters (b) Calculate the power of the eyeglass lens the child should use for relaxed distance vision. diopters Is the lens converging or diverging? converging diverging

Answer 1

Step-by-step explanation:

a ) image distance ( fixed ) = + 2 cm

object distance u₁ = - 12.5 cm

lens formula

1 / v - 1/ u₁ = 1 / f

1 / 2 + 1 / 12.5 = 1 / f

.5 + .08 = 1 / f

.58 = 1 / f

f = 1 / .58 cm = 1.724cm

= 1.724 / 100 m

power = 1 / f

power = 100 / 1.724

= 58 D

object distance u₂ = - 117 cm

lens formula

1 / v - 1/ u₂ = 1 / f

1 / 2 + 1 / 117 = 1 / f

.5 + .0085 = 1 / f

.5085 = 1 / f

f = 1 / .5085 cm = 1.9665cm

= 1.9665 / 100 m

power = 1 / f

power = 100 / 1.9665

= 50.85 D

Range of power 50.85 D to 58 D .

b ) for relaxed vision u = infinity

v = - 12.5 cm ; f = ?

1 / v - 1 / u = 1/ f

- 1 /12.5 - 0 = 1/f

f = - 12.5 cm

power = - 100 / 12.5

= - 8 D.

Since focal length is negative , len is concave.