AQA A-Level Physics Paper 3 (3BB), June 2025: Question 1

9 marks · Medium difficulty · Short Answer

Complete ray paths into the eye, identify the component enabling accommodation, calculate focal length at the near point using an accommodation graph, and explain hypermetropia variation with age.

Practise this question

Question

Question 01 consists of four parts related to the human eye. Part 01.1 shows Figure 1 with an outline of an eye, the cornea, lens, and optical axis, with two parallel incident rays to complete. Part 01.2 asks which part of the eye enables accommodation (options: cornea, iris, lens). Part 01.3 provides the formula A = 1/d1 - 1/d2 and a graph (Figure 2) plotting accommodation amplitude A in dioptres against age in years, showing A decreasing from over 13 dioptres at age 10 to about 1 dioptre at age 70; it asks to calculate the eye's focal length at the near point for a 30-year-old whose far point is at infinity and focal length at the far point is 23 mm. Part 01.4 asks to explain how Figure 2 supports the suggestion that hypermetropia increases with age.
Question text

01.1 Figure 1 shows a simplified diagram of an eye that has no sight defects.

The eye is viewing a distant point object.

Complete, on Figure 1, the paths of the two rays to the back of the eye.

[2 marks]

Figure 1

01.2 Accommodation is the ability of the eye to change its optical power.

Which part of the eye enables accommodation?

Tick ( ) one box.

[1 mark]

cornea

iris

lens 4

The accommodation amplitude A, in dioptres, is given by

A = −

d1 d2

*03*where

d1 is the distance, in m, from the eye to its near point

d2 is the distance, in m, from the eye to its far point.

Figure 2 shows how the value of A varies with age for a typical person.

Figure 2

01.3 An eye of a typical 30-year-old person has a far point at infinity.

The focal length of the eye when viewing an object at its far point is 23 mm.

Calculate the focal length of the eye when viewing an object at its near point.

[4 marks]

focal length = mm

01.4 For a typical person, the far point remains at infinity as the person’s age increases.

Some studies suggest that hypermetropia increases with age.

Explain how Figure 2 supports this suggestion.

[2 marks]

Mark scheme

Show the mark scheme Mark scheme for Question 01 detailing marks for 01.1 to 01.4 totaling 9 marks. 01.1 awards 2 marks for rays refracting at the cornea towards the optical axis, and refracting at the lens to converge at the retina along the optical axis. 01.2 awards 1 mark for ticking 'lens'. 01.3 awards 4 marks for finding A = 8.8 dioptres from Figure 2, calculating d1 = 114 mm (or 0.114 m), applying the lens formula 1/f = 1/u + 1/v with u = d1 and v = 23 mm, obtaining f = 19 mm. 01.4 awards 2 marks for defining hypermetropia / near point increase and linking it to decreasing A on the graph while far point d2 remains unchanged.

Question Answers Additional comments/Guidance Mark AO

01.1 Both rays refracted towards optical axis at cornea 1 2 AO1

Condone non-straight line for MP1 or MP2 but not

both.

Rays refracted towards optical axis at lens and meets at the

intersection of optical axis with back of eye and rays are

continuous between lens and back of eye 2

01.2 lens tick in 3rd box only; CAO 1 AO1

01.3 for 1 CAO Allow evidence of 8.8 on Figure 2 4 2 × AO2

( A =) 8.8 (dioptres) 1

for 2 expect to see 2 × AO3

Correctly calculates d1 from formula using their A 2

d1 = 114 (mm) allow 2 sf 110 (mm)

must see appropriate working., e.g.

15 1

allow d1 = Or d1 = Or (A=) 8.8 =

8.8 44 𝑑𝑑1

for 3 allow one POT error

use of the lens formula 3

EITHER Find v with object at far point,

11 1

6 e.g. = � � +

23 ∞ 𝑣𝑣

11 1

condone = � � +

𝑓𝑓 ∞ 23

expect to see v = 23 (mm)

OR Find focal length with object at near point,

11 1

e.g. = +

𝑓𝑓 𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑢𝑢 𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑣𝑣

expect to their u = their d1

Condone:

• u, v mix up

• allow either their u or their v but not both

penalise incorrect signs in 3

focal length correct 4 for 4 allow 19(.1) for d1 = 114 mm

and 19(.0) for d1 = 110 mm

Must see correct working in MP3 to support this

answer.

01.4 explains hypermetropia for 1 accept 2 1 × AO1

• cannot focus on nearby objects 1 × AO3

Or • light from nearby objects focused behind

retina

Interprets Figure 2 in terms of d1 OR A and d2 1 • near point further away / near point

increases

• idea that d1 increases

• A decreases and d2 does not change

Treat each bullet point as independent.

‘long-sighted’ is neutral

for 2

Describes the relationship between A and d1 therefore (Figure 2 shows) A decreases (with age) because

identifying how Figure 2 suggests hypermetropia increases d1 increases

with age 2

OR

(Figure 2 shows) A decreases (with age) because

decreases.

d1

any suggestion that d2 changes loses 2

For 12 , allow A referred to as ‘accommodation

amplitude’ but must refer to either d1 or for 2

d1

How to answer it

Optics of the Human Eye: Accommodation & Vision Defects

📋 What This Question Tests

This question assesses your understanding of medical physics and optics of the eye, specifically:

  • Ray optics of the unaccommodated eye: Refraction at the cornea and crystalline lens to form a focused image on the retina.
  • Mechanism of accommodation: Identifying the role of the crystalline lens and ciliary muscles in altering optical power.
  • Accommodation amplitude & lens formula calculations: Extracting data from graphs, relating near/far points to accommodation amplitude ( A = 1/d₁ − 1/d₂ ), and applying the thin lens equation ( 1/f = 1/u + 1/v ) with consistent unit conversions.
  • Defects of vision: Defining hypermetropia (long-sightedness) and explaining its physical relationship to near point recession with age.
Question 01.1 (2 Marks)

Ray Diagram for an Unaccommodated Normal Eye

Completing the ray paths for parallel rays entering the eye

✅ Mark Scheme Requirements

  • Mark 1: Both parallel incident rays refract towards the optical axis upon passing through the cornea.
  • Mark 2: Rays refract further towards the optical axis at the lens and converge exactly at the intersection of the optical axis and the retina (back of the eye). Rays must be continuous from the lens to the retina.

🧠 Diagram Instructions

Since this is a drawing task, your diagram should show:

  • Refraction happens in two distinct steps: first at the outer curved surface (cornea), and second at the crystalline lens.
  • Use a ruler. The rays must bend inwards at the cornea, bend inwards again at the lens, and meet sharply at a single focal point on the retina on the dashed optical axis line.

❌ Common Errors

  • Passing straight through the cornea: Many students draw straight rays from outside the eye right into the lens, ignoring the fact that ~two-thirds of the eye's refractive power occurs at the cornea!
  • Focusing in front of or behind the retina: A normal eye viewing a distant object (at infinity) focuses precisely on the retina.
Question 01.2 (1 Mark)

Mechanism of Accommodation

Identifying the structure that changes optical power

✅ Correct Answer

Tick the 3rd box only: lens [1 mark]

💡 Key Knowledge

Accommodation is the process by which the ciliary muscles alter the curvature and shape of the flexible crystalline lens to adjust its focal length, allowing objects at varying distances to be focused onto the retina.

Question 01.3 (4 Marks)

Calculation: Focal Length at Near Point

Using accommodation amplitude and the thin lens equation

📐 Step-by-Step Calculation

  1. Step 1: Read amplitude A from Figure 2 for age 30
    Locate 30 on the horizontal axis (age / years) and read the value on the curve:
    A = 8.8 D (dioptres) [1 mark]
  2. Step 2: Calculate the near point distance d₁
    The question states the far point is at infinity, so d₂ = ∞ , meaning 1/d₂ = 1/∞ = 0 .
    Using A = 1/d₁ − 1/d₂ :
    8.8 = 1/d₁ − 0 ⟹ d₁ = 1 / 8.8 ≈ 0.1136 m = 114 mm (or 110 mm to 2 s.f.) [1 mark]
  3. Step 3: Relate eye geometry to the thin lens equation
    When viewing a distant object ( u = ∞ ), the image is on the retina at image distance v . Since f_far = 23 mm :
    1/f = 1/u + 1/v ⟹ 1/23 = 1/∞ + 1/v ⟹ v = 23 mm (retina distance).
    Now set up the lens equation for the near point where u = d₁ = 113.6 mm (or 114 mm) and v = 23 mm :
    1/f = 1/u + 1/v = 1/113.6 + 1/23 [1 mark]
  4. Step 4: Solve for the near-point focal length f
    1/f = 0.00880 + 0.04348 = 0.05228 mm⁻¹
    f = 1 / 0.05228 = 19.1 mm (accept 19 mm or 19.0 mm depending on rounding of d₁ ) [1 mark]

❌ Common Errors & Traps

  • Unit mismatch: The amplitude formula requires d₁ in metres (because 1 D = 1 m⁻¹), but the eye lens focal length is given in millimetres. Mixing metres and millimetres without conversion causes massive power-of-ten errors.
  • Confusing u and v: The image distance v is fixed by the anatomy of the eye (distance from lens to retina = 23 mm). It does NOT change during accommodation; only u and f change.

🧠 Top Tip

Check physical realism: when viewing a close object, the eye lens becomes more curved (more powerful), so the focal length must become shorter than 23 mm. A result of ~19 mm makes complete physical sense!

Question 01.4 (2 Marks)

Explaining Hypermetropia & Ageing Trends

Linking Figure 2 to the definition of long-sightedness

✅ Mark Scheme Breakdown

  • Mark 1 (Understanding hypermetropia / interpreting Figure 2):
    Hypermetropia means an inability to focus on nearby objects (near point is further away / d₁ increases) OR Figure 2 shows A decreases with age while d₂ remains constant at infinity.
  • Mark 2 (Connecting the two):
    Figure 2 shows accommodation amplitude A decreases with age, and since A = 1/d₁ , this means near point distance d₁ increases, which corresponds to increasing hypermetropia (presbyopia).

🧠 Examiner Commentary

  • Do NOT just say "long-sighted": The mark scheme explicitly states that merely writing 'long-sighted' is neutral and scores no marks. Explain what happens optically (near point moves further away / light focuses behind retina).
  • Explicit link required: To get full marks, explicitly link the mathematical trend: as age increases, A decreases ➔ because 1/d₂ = 0 , 1/d₁ decreases ➔ therefore d₁ must increase.
  • Avoid stating that d₂ changes: The question clearly tells you the far point remains at infinity; stating that d₂ changes will forfeit Mark 2!

Topics

Optional topics · Practical skills · 3.10 Medical physics (A-level only) · Data analysis

Question and mark scheme from the AQA A-Level Physics examination, Paper 3 (3BB), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.