Sensitivity and Spectral Response of the Eye Revision Notes | A Level AQA Physics

1. The Eye as a Photodetector

Your eye is, at its core, a biological photodetector — a device that converts incoming light into an electrical signal. What makes it fascinating from a physics perspective is that it does not respond equally to all wavelengths of light. Its sensitivity varies dramatically across the visible spectrum, and that variation tells us a great deal about how it functions.

In medical physics, understanding the eye's spectral response matters because it underpins how we design lighting systems, display screens, and diagnostic instruments. Before we can appreciate those applications, we need to understand the physics of what the eye actually detects and how efficiently it does so at each wavelength.

The visible spectrum spans roughly 380 nm (violet) to 700 nm (red). Within that range, the eye does not treat all wavelengths equally — it is far more sensitive to some than others. This wavelength-dependent response is called the spectral response of the eye, and it is the central concept for this lesson.

2. Rod and Cone Cells: Two Detectors in One Eye

The retina contains two types of photoreceptor cells: rods and cones. Think of them as two separate detection systems operating in parallel, each optimised for different conditions. Understanding their individual spectral responses is the key to understanding the eye's overall sensitivity.

Rod cells are highly sensitive to light intensity but cannot distinguish between wavelengths — they give no colour information. They dominate vision in dim conditions, a mode called scotopic vision. Cone cells, by contrast, operate in bright light (photopic vision) and come in three types, each sensitive to a different region of the spectrum, giving us colour perception.

The three cone types are labelled S (short wavelength, peak ~420 nm), M (medium wavelength, peak ~530 nm), and L (long wavelength, peak ~560 nm). The brain interprets colour by comparing the relative outputs of these three cone populations — a process of differential signalling rather than direct wavelength measurement.

3. The Spectral Response Curve

The spectral response of the eye is represented as a graph of relative sensitivity against wavelength. There are two distinct curves: one for scotopic (rod-dominated) vision and one for photopic (cone-dominated) vision. Both curves are bell-shaped, but they peak at different wavelengths and shift relative to each other — a phenomenon known as the Purkinje shift.

Notice that the scotopic curve peaks at around 498 nm and falls steeply on both sides. The photopic curve peaks near 555 nm. At the red end of the spectrum (beyond about 650 nm), both curves approach zero — the eye has negligible sensitivity to deep red light, and essentially none beyond 700 nm.

The Purkinje shift describes the change in peak sensitivity as lighting conditions change from photopic to scotopic. In dim light, the peak shifts from 555 nm towards 498 nm. This is why, at dusk, red objects appear to dim faster than blue or green objects of the same luminance — the rods, which take over in low light, are far less sensitive to long wavelengths.

4. Sensitivity: What It Means Quantitatively

Sensitivity, in the context of the eye as a photodetector, refers to how effectively the eye converts incident light energy into a neural response. The relative sensitivity at any wavelength is normalised so that the peak value equals 1.0 (or 100%). All other wavelengths are expressed as a fraction of that peak.

This normalised sensitivity function is called the luminosity function, denoted $V(\lambda)$ for photopic vision and $V'(\lambda)$ for scotopic vision. These are internationally standardised curves defined by the Commission Internationale de l'Eclairage (CIE) and are used in the design of lighting, displays, and optical instruments.

A worked example helps to make this concrete. If the eye has a relative sensitivity of 0.06 at 620 nm (orange-red), this means that a light source at 620 nm must be roughly 17 times more intense than a source at 555 nm to produce the same perceived brightness. The eye is far less efficient at converting those longer-wavelength photons into a neural signal.

Worked example: Interpreting Relative Sensitivity from the Spectral Response Curve

A light source emits at 620 nm with an intensity of 1.0 W m⁻². A second source emits at 555 nm. What intensity must the 555 nm source have to produce the same perceived brightness as the 620 nm source? Use $V(620\text{ nm}) = 0.06$ and $V(555\text{ nm}) = 1.00$.

1. $V(\lambda)$ = fraction of peak response at wavelength $\lambda$ — A value of 0.06 at 620 nm means the eye is only 6% as sensitive there as at its peak (555 nm). To match the perceived brightness, the 555 nm source needs proportionally less intensity.
2. $I_{555} \times V(555) = I_{620} \times V(620)$ — Perceived brightness is proportional to intensity multiplied by relative sensitivity. For equal perceived brightness, these products must be equal.
3. $I_{555} \times 1.00 = 1.0 \times 0.06$ — The 620 nm source has intensity 1.0 W m⁻² and sensitivity 0.06. The 555 nm source has sensitivity 1.00.
4. $I_{555} = \frac{1.0 \times 0.06}{1.00} = 0.06 \text{ W m}^{-2}$ — The 555 nm source needs only 0.06 W m⁻² to appear equally bright. The eye is so much more sensitive at 555 nm that far less intensity is required.
5. $\frac{I_{620}}{I_{555}} = \frac{1.0}{0.06} \approx 17$ — The 620 nm source must be approximately 17 times more intense to match the perceived brightness of the 555 nm source. This confirms the eye's much lower efficiency at 620 nm.

Answer: The 555 nm source requires an intensity of 0.06 W m⁻² to match the perceived brightness of the 1.0 W m⁻² source at 620 nm.

5. Factors Affecting the Eye's Sensitivity

Several physical and physiological factors determine how sensitive the eye is at any given moment. From a physics standpoint, the most important are the wavelength of incident light, the intensity of illumination (which determines whether rods or cones dominate), and the degree of dark adaptation.

Dark adaptation is the process by which the eye increases its sensitivity after moving from a bright to a dim environment. Rod cells regenerate the photopigment rhodopsin, which bleaches (breaks down) in bright light. Full dark adaptation takes approximately 30 minutes and can increase the eye's sensitivity by a factor of around $10^4$ to $10^5$ compared to its photopic state.

• Wavelength: sensitivity follows the $V(\lambda)$ or $V'(\lambda)$ curve — peak at 555 nm (photopic) or 498 nm (scotopic)
• Illumination level: determines whether photopic (cone) or scotopic (rod) vision dominates
• Dark adaptation: rhodopsin regeneration in rods increases sensitivity over ~30 minutes in darkness
• Age: the lens yellows with age, absorbing more short-wavelength (blue-violet) light and reducing sensitivity at those wavelengths
• Retinal location: the fovea contains only cones, so peripheral vision (rod-rich) is more sensitive in low light

The fovea — the central region of the retina — is densely packed with cone cells and is responsible for high-acuity colour vision. It contains no rods at all. This is why, in very dim light, you can sometimes see a faint star more clearly by looking slightly to the side of it rather than directly at it: you are directing the image onto the rod-rich peripheral retina rather than the cone-only fovea.

6. The Eye Compared to Other Photodetectors

The eye is a remarkable detector, but it has clear limitations when compared to electronic photodetectors such as charge-coupled devices (CCDs) or photodiodes. Evaluating these differences is a common higher-order task in medical physics questions.

Electronic photodetectors can be designed to respond to a much wider range of wavelengths than the eye — from ultraviolet through to infrared — whereas the eye is restricted to roughly 380–700 nm. CCDs used in medical imaging can also produce a quantitative, linear output across their range, whereas the eye's response is logarithmic in nature (it compresses a huge range of intensities into a manageable perceptual range).

The logarithmic response of the eye is actually a significant advantage in everyday vision — it allows us to function across an enormous range of light intensities, from starlight to bright sunlight. However, for precise scientific measurement, this non-linearity is a serious limitation, which is why electronic detectors are preferred in medical imaging and spectroscopy.

7. Exam Technique and Common Mistakes

Questions on the eye's spectral response tend to test three things: recall of specific wavelength values, interpretation of sensitivity curves, and higher-order comparison or evaluation tasks. Here is how to approach each type precisely.

When a question asks you to describe the spectral response, give a sequential account: state the wavelength range of visible light, identify the peak sensitivity wavelength for the relevant condition (photopic or scotopic), and describe how sensitivity falls on either side of the peak. Do not use the word 'because' — describe is a 'what happens' command, not a 'why' command.

When asked to explain a feature of the spectral response — for example, why sensitivity is low at 650 nm — you must link the observation to the underlying mechanism: the photopigments in rod and cone cells absorb photons most efficiently at their characteristic wavelengths, and at 650 nm the absorption probability for all photopigments is low, so fewer photons trigger a neural response per unit intensity.

For evaluate or compare questions about the eye versus electronic detectors, structure your answer as: point — evidence — counter-point — conclusion. Avoid one-sided answers; examiners reward balanced judgement with a clear final statement.