Ray diagrams and calculations of powers (in dioptres) of correcting lenses…

The idea

Myopia is short sight: the eye converges too strongly or is too long, so parallel rays focus in front of the retina and distant objects blur. A diverging lens of negative power spreads rays before the eye, moving the focus back onto the retina. Hypermetropia is long sight: the eye is too weak or too short, so parallel rays would focus behind the retina and near objects blur. A converging lens of positive power adds convergence, bringing the focus forward. Lens power P is the reciprocal of focal length in metres, P = 1/f, measured in dioptres (D). In ray diagrams, draw the correcting lens in front of the eye, then show rays leaving it and focusing on the retina. For a distant object, the required power is found from the far point; for a near object, use the near point and the thin-lens equation.

What earns the marks

• Myopia is corrected with a diverging (concave) lens of negative power because the unaided eye focuses distant rays too soon.
• Hypermetropia is corrected with a converging (convex) lens of positive power because the unaided eye cannot converge near rays enough.
• Power is calculated using P = 1/f with focal length in metres, giving the unit dioptre (D).
• A correct ray diagram shows the lens in front of the eye, the object rays, and the final image formed on the retina.
• For myopia, the lens must form an image of a distant object at the eye's far point; for hypermetropia, it must help form an image of a near object on the retina.
• Sign conventions must be consistent: diverging lenses have negative focal lengths and powers, converging lenses positive.

Common mistakes and how to put them right

• Using centimetres directly in P = 1/f.

  Put it right: Convert focal length to metres before dividing, so 50 cm becomes 0.50 m and P = 2.0 D.

• Mixing up which lens corrects which defect.

  Put it right: Myopia needs a diverging lens and hypermetropia needs a converging lens.

• Drawing rays that cross before the lens or focus behind the retina.

  Put it right: Show the correcting lens acting first and the final focus on the retina.

Exam tips

• Write the power equation, substitute in metres, then give the answer with the correct sign and the unit D.
• Annotate ray diagrams with the lens type, the principal focus and the retinal image position to make the physics explicit.
• Check whether the question gives a far point or near point, because that determines which object distance you use in the calculation.