Sometimes a person cannot clearly see objects close up or far away. To correct this type of vision, bifocals are often used. The top half of the lens is used to view distant objects and the bottom half of the lens is used to view objects close to the eye. A person can clearly see objects only if they are located between 34 cm and 171 cm away from her eyes. Bifocal lenses are used to correct her vision. What power lens (in diopters) should be used in the bottom half of the lens to allow her to clearly see objects 25 cm away?

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aristocles aristocles · Answer 1 · 2019-08-19T02:35:23+02:00

Answer:

Top Half power is

[tex]P_{top} = -0.58 dioptre[/tex]

Bottom half power

[tex]P_{bottom} = +1.06 dioptre[/tex]

Explanation:

For the top part of the lens we need a focal length of the lens in which person can see upto a large distance

so here we have

[tex]d_i = -171 cm[/tex]

[tex]d_o = infinite[/tex]

now by lens formula

[tex]\frac{1}{d_i} + \frac{1}{d_o} = \frac{1}{f}[/tex]

now we have

[tex]f = d_i = -171 cm[/tex]

now power of top part of the lens is given as

[tex]P = \frac{1}{f} = -0.58 Dioptre[/tex]

Now for the bottom half we can say

[tex]d_o = 25 cm[/tex]

[tex]d_i = -34 cm[/tex]

now by lens formula

[tex]\frac{1}{25} - \frac{1}{34} = \frac{1}{f}[/tex]

[tex]f = 94.4 cm[/tex]

[tex]P = \frac{1}{f} = 1.06 Dioptre[/tex]