Physics of the eye (3.10.1)

The diagram below shows the internal structure of the human eye.

The parts of the eye include:

• Cornea: Light rays enter the eye through the cornea. It is a thin, transparent, convex window with a relatively high refractive index. The cornea is responsible for the majority of the eye’s focusing.

• Pupil: The dark opening at the centre of the eye. It is surrounded by the iris, which contains muscles that control how much light enters the eye by changing the size of the pupil, widening in the dark and contracting in bright light.

• Lens: It is used for finer focusing and is controlled by the ciliary muscles in the eye. When these muscles contract, the lens becomes thicker and more spherical (i.e. more powerful). When these muscles relax, the lens becomes thinner and flatter (i.e. less powerful). This changes the eye’s focal length.

• Retina: The retina contains light-sensitive cells called rods and cones, and is where the image is formed. The cells send signals via the optic nerve to the brain, enabling vision.

The retina, at the back of the eye, contains two main types of light-sensitive cells:

• rod cells
• cone cells.

These cells are called photoreceptors because they respond to light.

Rods and cones contain light-sensitive chemical pigments. When light is incident upon them, these pigments are activated and then become bleached.  This leads to electrical signals, which pass through nerve cells in the retina and then travel to the brain via the optic nerve.

The pigments are regenerated, or unbleached, by enzymes using vitamin A-containing substances from the blood.

There is one main type of rod cell and three types of cone cells.

Properties of rods:

• They detect light at low intensity.
• They give greyscale vision with little detail.
• There are about 120 million rods.
• Several rods connect to a single nerve fibre.

Properties of cones:

• They detect light at high intensity.
• There are three types: red, green and blue detecting cones.
• They provide detailed colour vision.
• There are about 5 million cones.
• A single cone connects to a single nerve fibre.
• They are highly concentrated in the fovea.

Cone cells are responsible for colour vision. The red, green and blue type cone cells are responsible for absorbing different ranges of light wavelengths.

The human eye is more responsive to red and green light. Thus, blue light often appears dimmer due to the reduced sensitivity. The brain receives signals from the three types of cone cells via the optic nerve and interprets their weighted strengths as colour.

It is useful to know that the human eye is more sensitive to red and green light because the eye’s optics scatter and absorb blue light more. Moreover, there is a higher concentration of red and green-sensitive cone cells in the central retina.

The plot below shows the weighted strengths vs. wavelength for the three types of cone cells.

Any colour can be interpreted by the brain as a combination of different intensities of red, green, and blue light.

For example, when receiving a strong signal from the red cones, a medium signal from the green cones, and no signal from the blue cones, the brain interprets this as yellow colour.

Spatial resolution is a measure of the eye’s ability to form separate images of objects that are close together.

The cells in the retina are responsible for distinguishing between different objects. Two objects can only be differentiated if there is at least one unactivated rod cell or cone cell between the light from each of the two objects.

If there is no inactive cell between the light from different objects, the brain cannot distinguish them and views them as a single object, as shown in the diagram below.

• The fovea, at the centre of the retina’s yellow spot, offers the sharpest vision due to densely packed, brain-connected cone cells.
• The yellow spot contains only cones, not rods. The area just outside the spot has many rods.
• In dim light, cones are ineffective, and rods take over. Since the yellow spot lacks rods, viewing faint objects directly is difficult. Looking slightly to the side shifts the image to rod-rich areas, improving detection.

The human eye contains a converging lens, so it brings the light rays entering the eye closer together.

When incident light rays are parallel to the principal axis, a converging lens focuses them to a single point, known as the principal focus, also called the focal point, as illustrated in the diagram below.

The focal length is the distance between the optical centre of the lens and the principal focus.

To find where the image is formed by a converging lens using a ray diagram drawn to scale.

The object is drawn as an arrow above the principal axis. Two light rays are drawn from the top of the object and pass through the lens, creating an image.

For a converging lens, the light rays obey the following rules:

• Light ray 1: This ray passes straight from the tip of the object through the centre of the lens, and its path is not affected.
• Light ray 2: This ray travels from the tip of the object to the lens parallel to the principal axis, and refracts towards the axis passing through the focal point on the other side of the lens.

The top of the image is formed where the two light rays meet.

To find the location of where an image is formed by a diverging lens, it is helpful to draw a ray diagram to scale.

The object is drawn as an arrow above the principal axis. Two light rays are drawn from the top of the object and pass through the lens, creating an image.

For a diverging lens, the light rays obey the following rules:

• Light ray 1: This ray travels from the tip of the object to the lens parallel to the principal axis and refracts away from the axis, appearing to have come from the principal focal point.
• Light ray 2: This ray passes from the tip of the object straight through the centre of the lens, and its path is not affected.

The top of the image is formed where the two light rays meet. The image formed through a diverging lens is virtual (i.e. it cannot be projected onto a screen) and upright.

The power of a lens is defined as its ability to refract light; the greater the power of a lens, the more light it refracts. This can also be applied to the lens of the eye:

Where:

• is the power of the lens in dioptres , and
• is the focal length .

Power and focal length are inversely proportional to each other. The shorter the focal length, the more powerful the lens, and vice versa.

Multiple parts of the eye are responsible for focusing light rays. Therefore, they can be combined and modelled as a single converging lens. The power of all these components can be summed to yield a single value for the eye’s power.

The power of the eye at the far point is equal to approximately , giving a focal length of This total power is the sum of:

• the cornea (around )
• the lens (around )

When the eye is focused on nearby objects, the eye’s power increases as the ciliary muscles contract, causing the lens to become thicker (more convex). As a result, the focal length decreases. However, the distance from the optical centre of the lens to the image remains essentially constant.

Lenses can produce either real or virtual images:

• A real image is formed when the light rays from an object converge at a point after passing through a lens. A real image can be projected onto a screen.
• A virtual image is formed when the light rays from an object appear to come from a point, but they do not actually meet or converge. A virtual image cannot be projected onto a screen.

Real and virtual images are created using a converging lens. However, a diverging lens can only form virtual images and cannot form a real image.

Converging lenses can produce both real and virtual images, depending on the object’s position relative to the lens. Therefore, converging lenses can have:

• a positive focal length if they produce a real image
• a negative focal length if they produce a virtual image.

Diverging lenses can only form virtual images and therefore have a negative focal length.

Short-sightedness, also known as myopia, describes people who can not focus on distant objects. This occurs when their far point is closer than infinity.

This is caused by the cornea and/or lens being too powerful or the eye being too long. The focusing power of the eye is too strong; therefore, rather than the image being formed on the retina, it forms in front of the retina.

To correct for short-sightedness, a diverging lens is used that has a principal focus at the eye’s incorrect far point. This lens has a negative focal length, and the focal length of the lens needs to be the same distance as the faulty eye’s far point.

Therefore, an object at infinity, which was initially out of focus, is now in focus at the far point. The diverging lens spreads the light rays before they enter the eye, which shifts the image formation further back onto the retina.

Long-sightedness, also known as hypermetropia, describes people who can not focus on close objects. This occurs when their near point is further away than normal.

It is caused by the cornea and/or lens being too weak or the eye being too short. The focusing power of the eye is too weak; therefore, rather than the image being formed on the retina, it forms behind the retina.

A converging lens must be used to correct for long-sightedness and to bring the image to a point further forward on the retina. This lens is required to produce images of objects away at the eye’s near point.

Therefore, close objects that were initially out of focus and are now in focus at the eye’s near point. A converging lens brings the light rays closer together before they enter the eye, which causes the formation of the image to move forward and onto the retina.

Astigmatism is caused by an irregularly shaped cornea and/or lens, resulting in different focal lengths for different planes.

A normal eye is shaped like a round ball, but with astigmatism, it is more like a rugby ball or an egg, distorting how light is focused onto the retina. For example, light rays in the horizontal plane may be in focus, but vertically oriented light rays may not be.

Astigmatism is corrected using a cylindrical lens. A cylindrical lens changes the refractive power in one plane only, while having little or no effect in the perpendicular plane. It is oriented so that it compensates for the eye’s unequal focusing power, bringing light rays from both planes to the same focus on the retina.

The prescription from an optician for a cylindrical lens describes the power needed to correct for short-sightedness or long-sightedness.

It also describes the power required to correct for astigmatism and the angle to the horizontal of the plane that does not require correction. An example prescription for an individual with astigmatism is shown in the table below.

• Sphere: the spherical component of the prescription. It is the amount of correction, in diopters, required to correct for the short-sightedness or the long-sightedness.
• Cylinder: the cylindrical component of the prescription, used to correct astigmatism. This value, measured in dioptres, can be positive or negative. If no astigmatism is present, this value is usually 0.00D or left blank.
• Axis: The axis specifies the orientation of the cylindrical lens. It is measured in degrees (from 1 to 180) using a protractor-like semicircle and specifies the lens’s angle within the frame.