Understanding Myopia and Corrective Lenses

Myopia, commonly known as nearsightedness, is a refractive error where distant objects appear blurry because the light focuses in front of the retina instead of directly on it. To correct myopia, a diverging lens is used, which is typically a concave lens. Concave lenses spread out light rays before they enter the eye, ensuring that the light focuses correctly on the retina.

The power of a lens is a measure of how much it converges or diverges light. It is defined as the reciprocal of the focal length of the lens, expressed in meters. The unit of power is the Dioptre (D).

The formula relating power (\(P\)) and focal length (\(f\)) is:

\(P = \frac{1}{f}\)

Where \(P\) is in Dioptres and \(f\) is in meters.

Calculating Focal Length for Myopia

We are given that the myopic person has a lens power of -1.25 Dioptre.

Given power \(P = -1.25\) D.

We can rearrange the formula to find the focal length \(f\):

\(f = \frac{1}{P}\)

Substituting the given power:

\(f = \frac{1}{-1.25} \text{ meters}\)

To calculate this value:

\(f = \frac{100}{-125} \text{ meters}\)

\(f = -0.8 \text{ meters}\)

The focal length is typically expressed in centimeters. To convert meters to centimeters, we multiply by 100:

\(f = -0.8 \times 100 \text{ cm}\)

\(f = -80 \text{ cm}\)

The calculated focal length is -80 cm.

Determining the Nature of the Lens

The power of the lens is given as -1.25 Dioptre, which is a negative value. The calculated focal length is -80 cm, which is also a negative value.

Lenses with negative power and negative focal length are diverging lenses. Diverging lenses are concave lenses.

As mentioned earlier, myopia is corrected using a concave lens to diverge the light rays.

Therefore, the nature of the lens is concave.

Summary of Findings

Based on the calculation, the focal length of the lens is 80 cm (the negative sign indicates the type of lens, not the magnitude often stated for the answer choice) and the nature of the lens is concave.

Let's compare this with the given options:

• 50 cm and convex lens
• 80 cm and convex lens
• 50 cm and concave lens
• 80 cm and concave lens

Our findings match the fourth option: 80 cm and concave lens.

Revision Table: Lens Power and Focal Length

Additional Information: Myopia and Vision Correction

Myopia is a common vision condition. For a myopic eye, the eyeball is usually slightly longer than normal, or the cornea is too curved. This causes light rays from distant objects to focus in front of the retina instead of directly on the retina.

Corrective lenses, like the concave lens discussed here, diverge the incoming light rays so that they focus further back, right on the retina. The stronger the myopia, the more diverging the lens needs to be, resulting in a higher negative power.

Other methods of correcting myopia include contact lenses and refractive surgery (like LASIK), which reshape the cornea to change its refractive power.