BIO Ordinary Glasses. Ordinary glasses are worn in front of the eye and usually 2.0 cm in front of the eyeball. Suppose that the person in Exercise 34.52 prefers ordinary glasses to contact lenses. What focal length lenses are needed to correct his vision, and what is their power in diopters?

Verified step by step guidance

1. Identify the object distance (distance from the glasses to the eye) and the image distance (distance from the eye to the retina). In this case, the object distance is -2.0 cm (negative because the object is virtual and located on the same side of the lens as the eye).
2. Determine the image distance required for normal vision. This is typically the distance from the lens to the retina. Assume a normal eye length of about 2.0 cm.
3. Use the lens formula to find the focal length of the glasses. The lens formula is \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \), where \( f \) is the focal length, \( d_o \) is the object distance, and \( d_i \) is the image distance.
4. Calculate the power of the lenses in diopters, which is given by the formula \( P = \frac{1}{f} \), where \( P \) is the power in diopters and \( f \) is the focal length in meters. Remember to convert the focal length from centimeters to meters before calculating the power.
5. Interpret the sign of the focal length and power. A positive focal length indicates converging lenses, which are used to correct farsightedness, while a negative focal length indicates diverging lenses, used to correct nearsightedness.

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. It is a critical parameter in optics that determines how strongly a lens converges or diverges light. For corrective lenses, the focal length is essential for ensuring that light focuses correctly on the retina, allowing for clear vision.

Lens Power

Lens power, measured in diopters (D), is the reciprocal of the focal length in meters. It indicates the degree of convergence or divergence of light by the lens. A positive power indicates a converging lens (convex), while a negative power indicates a diverging lens (concave). The power is crucial for determining the appropriate lens needed to correct vision.

Optical Correction

Optical correction involves using lenses to adjust the focal point of light entering the eye, compensating for refractive errors such as myopia (nearsightedness) or hyperopia (farsightedness). The goal is to ensure that light focuses directly on the retina, improving visual clarity. Understanding the relationship between the distance of the lens from the eye and the required focal length is vital for effective correction.