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The Human Eye and Optical Phenomena - DEFECTS OF VISION AND THEIR CORRECTION10.2 DEFECTS OF VISION AND THEIR CORRECTION10.2 DEFECTS OF VISION AND THEIR CORRECTION10.2 DEFECTS OF VISION AND THEIR CORRECTION10.2 DEFECTS OF VISION AND THEIR CORRECTION

Grade 10CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Refractive Defects: Sometimes the eye loses its power of accommodation, causing the vision to become blurred. This happens due to refractive defects like Myopia, Hypermetropia, and Presbyopia.

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Myopia (Near-sightedness): A person with myopia can see nearby objects clearly but cannot see distant objects distinctly. The image of a distant object is formed in front of the retina rather than on it.

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Causes of Myopia: This defect arises due to (i) excessive curvature of the eye lens, or (ii) elongation of the eyeball.

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Correction of Myopia: It is corrected by using a concave (diverging) lens of suitable power which brings the image back onto the retina.

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Hypermetropia (Far-sightedness): A person can see distant objects clearly but cannot see nearby objects distinctly. The near point for the person is farther away from the normal near point (25 cm25 \text{ cm}). The image of a nearby object is formed behind the retina.

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Causes of Hypermetropia: This defect arises because (i) the focal length of the eye lens is too long, or (ii) the eyeball has become too small.

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Correction of Hypermetropia: It is corrected by using a convex (converging) lens of appropriate power, which provides the additional focusing power required to form the image on the retina.

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Presbyopia: The power of accommodation of the eye usually decreases with aging. For most people, the near point gradually recedes. It arises due to the gradual weakening of the ciliary muscles and diminishing flexibility of the eye lens.

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Correction of Presbyopia: Often corrected using bifocal lenses, where the upper portion is a concave lens (for distant vision) and the lower part is a convex lens (for near vision).

📐Formulae

Lens Formula: 1f=1v−1u\text{Lens Formula: } \frac{1}{f} = \frac{1}{v} - \frac{1}{u}

Power of a Lens: P=1f (where f is in meters)\text{Power of a Lens: } P = \frac{1}{f} \text{ (where } f \text{ is in meters)}

For Myopia correction: f=−d (where d is the far point of the defective eye)\text{For Myopia correction: } f = -d \text{ (where } d \text{ is the far point of the defective eye)}

For Hypermetropia correction: 1f=1−d−1−0.25 (where d is the near point in meters)\text{For Hypermetropia correction: } \frac{1}{f} = \frac{1}{-d} - \frac{1}{-0.25} \text{ (where } d \text{ is the near point in meters)}

💡Examples

Problem 1:

The far point of a myopic person is 80 cm80 \text{ cm} in front of the eye. What is the nature and power of the lens required to correct the problem?

Solution:

To correct myopia, the object at infinity (u=−∞u = -\infty) must form a virtual image at the person's far point (v=−80 cm=−0.8 mv = -80 \text{ cm} = -0.8 \text{ m}). Using lens formula: 1f=1v−1u\frac{1}{f} = \frac{1}{v} - \frac{1}{u} 1f=1−0.8−1−∞\frac{1}{f} = \frac{1}{-0.8} - \frac{1}{-\infty} 1f=−1.25+0\frac{1}{f} = -1.25 + 0 f=−0.8 mf = -0.8 \text{ m} P=1f=1−0.8=−1.25 DP = \frac{1}{f} = \frac{1}{-0.8} = -1.25 \text{ D}

Explanation:

A concave lens of power −1.25 D-1.25 \text{ D} is required. The negative sign indicates a diverging (concave) lens.

Problem 2:

A person with a hypermetropic eye has a near point of 1 m1 \text{ m}. What is the power of the lens required to correct this defect? (Assume normal near point is 25 cm25 \text{ cm})

Solution:

Here, the object is placed at the normal near point u=−25 cm=−0.25 mu = -25 \text{ cm} = -0.25 \text{ m}. The image should be formed at the defective near point v=−1 mv = -1 \text{ m}. Using lens formula: 1f=1v−1u\frac{1}{f} = \frac{1}{v} - \frac{1}{u} 1f=1−1−1−0.25\frac{1}{f} = \frac{1}{-1} - \frac{1}{-0.25} 1f=−1+4\frac{1}{f} = -1 + 4 1f=+3 D\frac{1}{f} = +3 \text{ D} P=+3.0 DP = +3.0 \text{ D}

Explanation:

A convex lens of power +3.0 D+3.0 \text{ D} is required to shift the image of the object from behind the retina onto the retina.