Defects of vision and their correction using lenses (A-level only) — AQA A-Level Physics

This topic covers common defects of vision, specifically myopia (short-sightedness) and hypermetropia (long-sightedness), and how lenses are used to correct them. You will learn the ray diagrams for each defect, the type of lens required, and how to calculate the power of the correcting lens using the lens formula and the concept of the far point and near point.

Understanding these defects is crucial because it applies the principles of refraction and lenses to a real-world biological context. It also forms the basis for more advanced optics in A-level Physics, such as the eye as an optical system and the use of lenses in instruments like telescopes and microscopes.

• →Myopia (short-sightedness): the eye focuses distant objects in front of the retina; corrected with a diverging (concave) lens of negative power.
• →Hypermetropia (long-sightedness): the eye cannot focus near objects on the retina; corrected with a converging (convex) lens of positive power.
• →The far point is the furthest distance a myopic eye can see clearly; the near point is the closest distance a hypermetropic eye can see clearly.
• →The power of a lens is P = 1/f, measured in dioptres (D), where f is in metres. Converging lenses have positive power, diverging lenses have negative power.
• →The lens formula 1/f = 1/v - 1/u is used to calculate the focal length of the correcting lens, with sign conventions: real objects have negative u, virtual images have negative v.

• 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.
• Astigmatism is caused by unequal curvature of refracting surfaces in different meridians, giving the eye two different focal powers.
• A prescription specifies a spherical power to correct one principal meridian and a cylindrical power equal to the difference between the two meridional powers.
• The axis is an angle in degrees that identifies the orientation of the cylindrical lens; its refractive power acts perpendicular to this axis.
• Standard notation uses DS for spherical power, DC for cylindrical power and × followed by the axis angle.
• Pure astigmatism can be corrected using only a cylindrical lens, meaning the spherical component is 0.00 DS.
• Powers are measured in dioptres, where the dioptre is the reciprocal of focal length in metres.

• 💡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.
• 💡Practise reading a sample prescription aloud, identifying the spherical power for one meridian and the cylindrical power difference.
• 💡Sketch the two principal meridians and show how the cylindrical lens adds extra power perpendicular to its axis.
• 💡Always state the type of lens and its power sign (positive or negative) when describing correction. Marks are often awarded for correct sign and lens type.
• 💡In ray diagrams, use arrows to show direction of light and label the retina, lens, and focal point clearly. Ensure the rays converge on the retina after correction.
• 💡When calculating power, show your working clearly: convert all distances to metres, substitute into the lens formula with correct signs, and round to an appropriate number of significant figures.

• Using centimetres directly in P = 1/f; correction: 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; correction: myopia needs a diverging lens and hypermetropia needs a converging lens.
• Drawing rays that cross before the lens or focus behind the retina; correction: show the correcting lens acting first and the final focus on the retina.
• Stating the spherical component corrects the average focus: correct this by specifying it corrects the refractive error in one principal meridian.
• Assuming the cylindrical power acts along the axis angle: correct this by remembering that a cylindrical lens applies its power perpendicular to its axis.
• Omitting the axis angle or treating it as a power value: the axis is an orientation in degrees, not a dioptre value.
• Students often think that a magnifying glass (convex lens) can correct myopia. Correction: myopia requires a diverging lens to spread rays, not a converging lens.
• Students sometimes believe that the far point of a myopic eye is at infinity. Correction: the far point is finite and closer than infinity; it is the distance at which the eye can focus without accommodation.
• Students may forget that the correcting lens for hypermetropia must form a virtual image at the near point, not a real image. Correction: the image is virtual and on the same side as the object, so v is negative in the lens formula.

1. 1Day 1: Review the structure of the eye and the basic principles of refraction and lenses. Watch a video on myopia and hypermetropia.
2. 2Day 2: Learn the ray diagrams for both defects and their correction. Practice drawing them with correct labels and arrows.
3. 3Day 3: Study the lens formula and power calculations. Work through examples for both myopia and hypermetropia, paying attention to sign conventions.
4. 4Day 4: Complete past paper questions on this topic. Focus on explanations and calculations. Check your answers against mark schemes.
5. 5Day 5: Create flashcards for key terms and formulas. Test yourself on common misconceptions and examiner tips.

• 📋Ray diagram questions: Draw a ray diagram to show how a diverging lens corrects myopia. Advice: Use a ruler, label the retina, lens, and focal point, and show the rays converging on the retina after the lens.
• 📋Calculation questions: Calculate the power of the correcting lens for a given far point or near point. Advice: Convert distances to metres, use the lens formula with correct signs, and state the unit (D).
• 📋Explanation questions: Explain why a person with hypermetropia cannot see near objects clearly and how a converging lens corrects this. Advice: Refer to the image forming behind the retina and the lens providing extra convergence.
• 📋Comparison questions: Compare and contrast myopia and hypermetropia in terms of causes, effects, and correction. Advice: Use a table or structured paragraphs, mentioning lens type, power sign, and far/near points.