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 type of vision problem: The person can see clearly up close but not beyond 75.0 cm, indicating nearsightedness or myopia. This condition is corrected using diverging lenses.
2. Determine the far point of the person's vision: The farthest distance at which objects are in clear focus is given as 75.0 cm. Convert this distance to meters by dividing by 100 (since 1 m = 100 cm).
3. Calculate the focal length of the lens needed: For a diverging lens, the focal length (f) should be negative and have a magnitude such that it allows the person to see distant objects clearly. Use the lens formula \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \), where \( d_o \) is the object distance (infinity for distant objects) and \( d_i \) is the image distance (equal to the far point).
4. Compute the power of the lens: The power (P) of a lens in diopters is given by the formula \( P = \frac{1}{f} \), where f is the focal length in meters. Remember to keep the sign of the focal length in mind when calculating power.
5. Summarize the findings: The focal length calculated will be the required focal length for the contact lenses, and the power calculated will be the diopter value needed to correct the person's myopia.

Key Concepts

Focal Length

Focal length is the distance from the lens to the point where parallel rays of light converge or appear to diverge. For corrective lenses, the focal length determines how strongly the lens bends light to focus images on the retina. In this case, the focal length needed can be calculated based on the distance at which the person can see clearly.

Lens Power

Lens power is a measure of the lens's ability to converge or diverge light, expressed in diopters (D). It is calculated as the inverse of the focal length in meters (P = 1/f). A positive power indicates a converging lens (for hyperopia), while a negative power indicates a diverging lens (for myopia). This concept is essential for determining the appropriate lens to correct the person's vision.

Optical Correction

Optical correction involves using lenses to adjust the focal point of light entering the eye, allowing individuals to see clearly at various distances. In this scenario, the person has difficulty focusing on distant objects, indicating hyperopia (farsightedness). Corrective lenses help to shift the focal point back onto the retina, enabling clear vision for distant objects.