The near point of a patient s eye is 50 0 cm Wh... - JAMB Physics 2023 Question

To determine the power of the corrective lens needed, you can use the lens formula:

\[ \text{Lens Power} = \frac{1}{\text{Focal Length}} \]

The focal length of the lens required to enable the eye to see an object clearly at a certain distance can be found using the lens formula:

\[ \frac{1}{\text{Focal Length}} = \frac{1}{\text{Image Distance}} - \frac{1}{\text{Object Distance}} \]

In this case, the near point of the patient's eye is the object distance, and the distance at which the patient wants to see clearly is the image distance.

Given:
- Object Distance (\(u\)) = 50.0 cm (near point)
- Image Distance (\(v\)) = 25.0 cm (desired distance)

Using the lens formula:

\[ \frac{1}{\text{Focal Length}} = \frac{1}{v} - \frac{1}{u} \]

\[ \frac{1}{\text{Focal Length}} = \frac{1}{25 \, \text{cm}} - \frac{1}{50 \, \text{cm}} \]

Now, calculate the values:

\[ \frac{1}{\text{Focal Length}} = \frac{2}{50} - \frac{1}{50} = \frac{1}{50} \]

So, the focal length (\(f\)) is 50.0 cm.

Now, use the lens power formula:

\[ \text{Lens Power} = \frac{1}{\text{Focal Length}} \]

\[ \text{Lens Power} = \frac{1}{50 \, \text{cm}} \]

Convert the units to diopters:

\[ \text{Lens Power} = \frac{1}{0.5 \, \text{m}} \]

\[ \text{Lens Power} = 2 \, \text{diopters} \]

Therefore, the correct answer is 2 diopters.