Question

Alice is farsighted and cannot see objects clearly that are closer to her eye than 80.0 cm. What is the refractive power of the contact lenses that will enable her to comfortably see objects at a distance of 25.0 cm from her eyes?

Answer 1

The refractive power of the contact lenses that will enable her to comfortably see objects at distance of 25.0 cm from her eyes is 2.75 D

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Further explanation

We will solve this problem using following formula:

$\large{ \boxed {\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}}}$

where:

so = distance of object from lens

si = distance of image from lens

f = focal length of lens

Let's tackle the problem!

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Given:

distance of object = s_o = 25.0 cm = 0.25 m

distance of image = s_i = -80.0 cm = -0.80 m ( virtual image )

Unknown:

refractive power = P = ?

Solution:

$\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}$

$\frac{s_o + s_i}{s_o s_i} = P$

$\large { \boxed {P = \frac{s_o + s_i}{s_o s_i}} }$

$P = \frac{0.25 - 0.80}{0.25 (-0.80)}$

$P = \frac{-0.55}{-0.2}$

$P = 2.75 \texttt{ D}$

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Conclusion:

The refractive power of the contact lenses that will enable her to comfortably see objects at distance of 25.0 cm from her eyes is 2.75 D

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Learn more

• Compound Microscope : brainly.com/question/7512369
• Reflecting Telescope : brainly.com/question/12583524
• Focal Length : brainly.com/question/8679241
• Mirror an Lenses : brainly.com/question/3067085

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Answer details

Grade: High School

Subject: Physics

Chapter: Light

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Keywords: Light , Mirror , Magnification , Ray , Diagram , Image , Real , Virtual

Answer 2

Answer:

The refractive power of the contact lenses is 2.75 D

Explanation:

Given that,

Image distance v = -80.0 cm

Object distance u= -25 cm

We need to calculate the refractive power

Using lens's formula

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

Where, v = Image distance

u = Object distance

$\dfrac{1}{f}=\dfrac{1}{-80}-\dfrac{1}{-25}$

$\dfrac{1}{f}=\dfrac{11}{400}\ cm^{-1}$

$\dfrac{1}{f}=\dfrac{11}{4}\ m^{-1}$

The refractive power of the contact lenses

$D=\dfrac{1}{f}$

$D=\dfrac{11}{4}$

$D=2.75\ diopters$

Hence, The refractive power of the contact lenses is 2.75 D.