The eye, the ear, ECG and endoscopy

What the exam asks

• The eye: ray diagrams, rods and cones (sensitivity, colour, resolution) and the cones’ spectral response.
• Defects of vision: myopia, hypermetropia and astigmatism; correcting-lens powers in dioptres; astigmatism prescriptions.
• The ear: structure and transmission, equal loudness curves, intensity level in dB and dBA, and hearing loss from noise and age.
• The ECG: obtaining the signal and explaining the shape of the normal waveform.
• Endoscopy: total internal reflection in fibres, coherent and non-coherent bundles, and keyhole surgery.

Core ideas

The eye as an optical system

Light is refracted at the cornea and then by the lens, forming a real, inverted image on the retina. The cornea provides about two-thirds of the eye’s power (roughly 40 D of about 60 D), because the refractive index changes most at the air–cornea boundary. The lens provides the adjustable part, called accommodation: the ciliary muscles contract to make it fatter and more powerful for near objects. The normal near point is 25 cm and the normal far point is infinity.

Rods, cones and resolution

Colour is decided by the ratio of the three cone responses. Light of 580 nm stimulates red cones strongly, green cones moderately and blue cones hardly at all, and the brain reads that as yellow. There is only one type of rod, so in dim light colours cannot be told apart.

Spatial resolution. Two point images are seen as separate only if at least one unstimulated cone lies between the two stimulated cones. Many rods share one nerve fibre, so the brain cannot tell which rod in a group was stimulated, and resolution away from the fovea is poor.

Lenses, power and the sign convention

Power is in dioptres (D) only when $f$ is in metres. Use the real-is-positive convention: real objects, real images and converging lenses are positive, while virtual images and diverging lenses are negative. A correcting lens forms a virtual image at a place where the eye can focus, so $v$ is negative.

An astigmatism prescription gives three things: the spherical power in D (correcting myopia or hypermetropia), the cylindrical power in D, and the axis of the cylinder in degrees, from 0° to 180°, measured anticlockwise from the horizontal as seen from in front of the patient. For example: sphere $-1.50$ D, cylinder $-0.75$ D, axis $30^\circ$.

The ear

• Outer ear: the pinna and auditory canal channel sound to the eardrum (tympanic membrane), which vibrates.
• Middle ear: the ossicles (hammer, anvil and stirrup) act as a lever, increasing the force about 1.3 to 1.5 times, and pass the vibrations to the much smaller oval window. Since pressure = force ÷ area, the area ratio (about 15 to 20) and the lever together raise the pressure about 20 to 25 times. This matches vibrations in air to the cochlear fluid, which is much harder to set vibrating; otherwise most of the energy would be reflected. The Eustachian tube equalises the air pressure on each side of the eardrum.
• Inner ear: in the fluid-filled cochlea, the basilar membrane resonates at different positions for different frequencies (high frequencies near the oval window). Hair cells there produce electrical signals in the auditory nerve.

Intensity, decibels and loudness

Intensity is the power per unit area at right angles to the wave’s direction, in $\text{W m}^{-2}$. The ear responds from $10^{-12}$ to about $1\ \text{W m}^{-2}$, and perceived loudness grows roughly with the of intensity, so a logarithmic scale is used:

• Doubling the intensity adds 3 dB. Multiplying it by 10 adds 10 dB, and by 100 adds 20 dB.
• Equal loudness curves join sounds of different frequencies that seem equally loud. The loudness in phons equals the intensity level of a 1 kHz tone that sounds equally loud. The lowest curve is the threshold of hearing. The ear is most sensitive at about 3–4 kHz and responds from about 20 Hz to 20 kHz.
• The dBA scale weights intensity levels to match the ear’s frequency response, so it reflects perceived loudness. Noise regulations use dBA.

Hearing loss shows up as a raised threshold. Noise exposure causes loss concentrated around 3–6 kHz, typically a dip near 4 kHz with some recovery above it. Age causes loss that increases steadily with frequency.

The ECG

Heart-muscle cells depolarise (the inside of the membrane swings from about −70 mV to positive) and then repolarise. Depolarisation starts at the sinoatrial (SA) node, spreads across the atria, is delayed at the atrioventricular (AV) node and then spreads through the ventricles. The combined signal at the skin is about 1 mV.

• P wave: atrial depolarisation, which leads to atrial contraction.
• QRS complex: ventricular depolarisation, which leads to ventricular contraction. The atria repolarise at the same time, but this is hidden by the QRS complex.
• T wave: ventricular repolarisation, as the ventricles relax.

Heart rate in beats per minute $= \dfrac{60}{\text{R–R interval in seconds}}$.

Getting a clean signal: electrodes go on the limbs and chest. Clean the skin (remove hair and dead skin) and use conductive gel for a low contact resistance. Keep the patient relaxed and still so skeletal-muscle signals do not swamp the trace. Use a high-gain amplifier with a high input impedance, screened leads and a filter for mains interference.

Fibre optics and endoscopy

Light stays in the core by total internal reflection at the core–cladding boundary, where $\sin c = \dfrac{n_\text{cladding}}{n_\text{core}}$. The lower-index cladding protects the core surface from scratches and stops light crossing between touching fibres, which would scramble the image.

A flexible endoscope contains:

• a non-coherent bundle carrying light in to illuminate the area. The fibres need not stay in order, so it is cheaper.
• a coherent bundle carrying the image out. Its fibres are in the same relative positions at both ends, so each carries one “pixel”. An objective lens at the tip forms an image on the bundle’s end, viewed through an eyepiece or camera. Thinner fibres give finer resolution.
• channels for water (cleaning the lens), air or CO₂ (inflating the cavity) and instruments such as forceps or a laser fibre for keyhole surgery.

Keyhole surgery needs only small incisions, so patients have less pain, blood loss, scarring and infection risk, and recover faster.

Worked examples

Exam technique

• Lenses: write the lens equation and substitute with signs before calculating, e.g. “$u = +0.25$ m, $v = -1.2$ m”. The method mark is for the correct signs. Convert cm to m first.
• Ratios of intensities: use $\frac{I_2}{I_1} = 10^{\Delta L/10}$, where is the difference in dB.

Common mistakes

Quick recap

• The cornea does most of the refracting; the lens accommodates.
• Rods are sensitive but give no colour and poor resolution (shared nerve fibres). Cones give colour and detail at the fovea.
• $P = \frac{1}{f}$ with $f$ in metres. Real is positive, so virtual images are negative. Myopia needs a diverging lens, hypermetropia a converging lens and astigmatism a cylindrical lens.
• Intensity level $=$. Doubling the intensity adds 3 dB. dBA weights the scale for the ear’s response. Noise loss dips near 4 kHz; age loss rises with frequency.