A short-sighted person's far point is 95cm. The defect can be corrected using

Analysis of the Question

The question describes a person with short-sightedness (myopia). A person with this defect can see near objects clearly but cannot see distant objects beyond a certain point (the far point). To correct this, we need to use a lens that will take an object at infinity (where a normal eye should see) and form a virtual image at the person's actual far point.

Concept Explanation

1. The Defect: Myopia occurs when the eyeball is too long or the lens is too powerful, causing light from distant objects to focus in front of the retina.
2. The Correction: We use a diverging lens (concave lens) to spread out the light rays before they enter the eye, effectively moving the image back onto the retina.
3. The Formula: We use the thin lens formula: $$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$ • $u$ (Object distance): Since we want the person to see objects at infinity, $u = \infty$. • $v$ (Image distance): The lens must form a virtual image at the person's far point. Since it is a virtual image, $v = -95\text{ cm}$. • $f$ (Focal length): This is what we need to find.

Step-by-Step Solution

1. Substitute the values into the lens formula: $$\frac{1}{f} = \frac{1}{\infty} + \frac{1}{-95}$$
2. Recall that $\frac{1}{\infty} = 0$: $$\frac{1}{f} = 0 - \frac{1}{95}$$ $$\frac{1}{f} = -\frac{1}{95}$$
3. Solving for $f$: $$f = -95\text{ cm}$$
4. The negative sign indicates that the lens is diverging (concave). Therefore, a diverging lens with a focal length of 95 cm is required.

Conclusion

Comparing our result to the given options, the correct choice is a diverging lens with a focal length of 95 cm.

Exam Tip

Always remember: Myopia is corrected with a Concave (Diverging) lens, and Hypermetropia (long-sightedness) is corrected with a Convex (Converging) lens. A quick mnemonic is "Myopia" has 6 letters, and "Concave" has 7; "Hypermetropia" is a long word, and "Convex" is a short word—or simply remember the acronym "CON-CAVE" for the "near" defect!