Question
A myopic person wears a concave lens of power −2 D. What is the far point of this person's eye?
Solution — Step by Step
Convert Power to Focal Length
Power and focal length are related by:
where is in metres. So:
The negative sign tells us it's a concave (diverging) lens — exactly what myopia needs.
Understand What the Lens is Actually Doing
The corrective lens is designed so that an object at infinity (very far away) forms a virtual image at the person's far point. We use the lens formula:
For an object at infinity, , so .
Apply the Lens Formula
Substituting into the lens formula:
The image forms at −50 cm — on the same side as the object, which is exactly what a virtual image from a concave lens does.
State the Far Point
Since the lens forms the image of a distant object at cm, the eye sees this image clearly. This means the eye itself can see clearly up to 50 cm — that's the far point.
Far point of this person's eye = 50 cm from the eye.
Why This Works
A healthy eye can see clearly up to infinity — its far point is at infinity. In myopia, the eyeball is slightly elongated, so the lens system converges light too strongly, focusing distant objects in front of the retina rather than on it.
The concave corrective lens diverges incoming parallel rays (from infinity) before they enter the eye. It makes them appear to come from a point 50 cm away — which is exactly where this person's eye can focus naturally. The lens "shifts" the effective object distance from infinity to 50 cm.
This is the key insight: the power of the corrective lens directly tells us where the far point is. D means far point at 50 cm, D means far point at 100 cm, and so on. Stronger myopia → larger magnitude power → closer far point.
Alternative Method
We can arrive at the answer without the lens formula by reasoning from the definition of the far point directly.
A concave lens of focal length cm, when object is at infinity, produces an image at its own focal point. That's a fundamental property of a diverging lens — rays parallel to the principal axis diverge and appear to come from the focal point.
So the image of any object at infinity is at = 50 cm in front of the lens. Since the person can see this image clearly, their far point is 50 cm.
💡 Expert Tip
For myopia problems, skip the formula altogether when the object is at infinity: far point = |focal length| = |1/P|. This saves 30 seconds in an exam.
Common Mistake
⚠️ Common Mistake
Students often write the far point as "−50 cm" because cm from the lens formula. The negative sign is just a sign convention (virtual image, same side as object) — it does not mean the far point is behind the eye or in some negative direction. Distance is always positive. The far point is 50 cm from the eye, full stop. Writing −50 cm will cost you marks in CBSE board evaluation.