Hypermetropia and Presbyopia: Class 10 Science

Quick answer: In hypermetropia (far-sightedness) a person sees distant objects clearly but not nearby ones, because the near point is farther than 25 cm. It happens when the focal length of the eye lens is too long or the eyeball is too short, so light from a near object focuses behind the retina. A convex lens corrects it. Presbyopia is the loss of near vision with age, caused by weakening ciliary muscles and a less flexible eye lens; it is also corrected with a convex lens, and people with both near and far defects may need bifocal lenses.

Hypermetropia

A hypermetropic person often holds a book farther away to read it.

Causes (NCERT)

1. The focal length of the eye lens is too long, so the lens does not converge light strongly enough.
2. The eyeball has become too small (too short from front to back).

How a convex lens corrects hypermetropia

Step 1: The convex lens converges the light from a book held at 25 cm before it enters the eye.

Step 2: It forms a virtual image of the book at the person's near point, which the eye can see clearly.

Step 3: The eye lens then focuses the light from that image on the retina.

 Without lens: object at 25 cm
   -> image forms behind retina

 With convex lens:
   -> image forms on retina

Finding the power of the lens

Use $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ with $u = -25$ cm (the book) and $v = -d$ (the defective near point, $d$ in cm):

$\frac{1}{f} = \frac{1}{25} - \frac{1}{d} = \frac{d - 25}{25d}$

Since $d > 25$, $f$ is positive, so the lens is convex and the power is positive.

Worked example

The near point of a hypermetropic eye is 50 cm. Find the power of the lens needed to read at 25 cm.

Step 1: $u = -25$ cm and $v = -50$ cm.

Step 2: $\frac{1}{f} = \frac{1}{-50} - \frac{1}{-25} = \frac{-1 + 2}{50} = \frac{1}{50}$, so $f = 50$ cm $= 0.5$ m.

Step 3: $P = \frac{1}{f} = \frac{1}{0.5} = +2$ D.

Answer: A convex lens of power +2.0 D. (For a near point of 1 m, the same method gives +3.0 D.)

Presbyopia

Presbyopia is the gradual decrease in the eye's power of accommodation with age. Most older people find it hard to see nearby objects clearly without glasses.

The near point moves farther away, so presbyopia is corrected with a convex lens.

Bifocal lenses

Sometimes a person has both myopia and hypermetropia. Such people need bifocal lenses:

Summary table

Exam tips

• Learn the two causes of hypermetropia in NCERT's words; they are often asked directly.
• In ray diagrams, show the image behind the retina for the defective eye and on the retina with the convex lens.
• In numericals, take $u = -25$ cm for hypermetropia, not $-\infty$.

Common mistakes

• Saying a hypermetropic person cannot see distant objects. They see distant objects clearly.
• Using a concave lens for hypermetropia.
• Confusing presbyopia (caused by age) with hypermetropia (caused by eyeball or lens shape).
• Forgetting to convert the focal length into metres before finding the power.

Frequently Asked Questions

What is hypermetropia?

It is a defect of vision in which a person can see distant objects clearly but cannot see nearby objects distinctly, because the near point is beyond 25 cm.

What are the causes of hypermetropia?

The focal length of the eye lens is too long, or the eyeball has become too small.

How is hypermetropia corrected?

With a convex lens of suitable power, which forms an image of nearby objects at the person's near point.

What causes presbyopia?

The ciliary muscles gradually weaken and the eye lens becomes less flexible with age, reducing the power of accommodation.

What is a bifocal lens?

A lens whose upper part is concave for distant vision and lower part is convex for near vision.