BIO A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. (c) What focal length contact lens is needed, and what is its power in diopters?

Verified step by step guidance

1. Identify the problem: The person has a near point of 75.0 cm, meaning they cannot see objects clearly beyond this distance. We need to find the focal length of the contact lens that will allow them to see distant objects clearly.
2. Understand the concept: The focal length of a lens is related to its power, which is measured in diopters. The power (P) of a lens is given by the formula: \( P = \frac{1}{f} \), where \( f \) is the focal length in meters.
3. Determine the desired focal length: Since the person wants to see distant objects clearly, the lens should focus parallel rays (from distant objects) onto the retina. This means the focal length of the lens should be equal to the person's far point, which is 75.0 cm or 0.75 meters.
4. Calculate the power of the lens: Use the formula for power \( P = \frac{1}{f} \). Substitute \( f = 0.75 \) meters into the formula to find the power in diopters.
5. Interpret the result: The calculated power will be a positive value, indicating a converging lens is needed. This power value in diopters is what the optometrist will use to prescribe the correct contact lenses.

Key Concepts

Focal Length

Focal length is the distance between the lens and the point where it converges or diverges light to form a clear image. It is crucial in determining how lenses correct vision. For a person who cannot see beyond a certain distance, the focal length of corrective lenses must be calculated to adjust the focus to infinity, allowing clear vision at all distances.

Lens Power

Lens power, measured in diopters, is the inverse of the focal length in meters. It indicates the degree to which a lens can converge or diverge light. A positive diopter value indicates a converging lens, used for farsightedness, while a negative value indicates a diverging lens, used for nearsightedness. Calculating the correct power is essential for effective vision correction.

Near Point and Far Point

The near point is the closest distance at which the eye can focus on an object, while the far point is the furthest distance. For someone who cannot focus beyond 75.0 cm, this distance is their far point. Corrective lenses adjust the far point to infinity, allowing the person to see distant objects clearly. Understanding these points helps in determining the necessary lens specifications.