10.1.6 Defects of Vision

Short-sightedness

• Short-sightedness is also called myopia
• It happens when the lens is more curved than normal
  • So the cornea and lens are too powerful
  • Myopia can also occur if the eyeball is too long
• This means light rays are refracted too much so the focal point of the image falls in front of the retina (rather than on it)
  • So distant objects appear blurry as people with short-sightedness cannot focus on distant objects

Ray Diagram of Short-Sightedness

An eye that is short-sighted has a wider lens with a larger focussing power so the light rays meet and form an image in front of the retina and not on it

Treatment of Short-sightedness

• Short-sightedness can be corrected using contact lenses or glasses with a diverging (concave) lens
  • The lens causes the light rays to diverge before reaching the eye
  • So when they are focussed by the eye the image now forms on the retina
• Remember from 10.1.1 Converging & Diverging Lenses that
  • Diverging lenses have a negative focal length and a negative power
• A short-sighted person can remove their glasses if they wish to read or view something close-up because it is easy for them to focus on objects close to the eye

The Effect of a Diverging Lens on a Short-sighted Eye

The diverging lens causes the rays to diverge before they reach the eye, so the image is formed on the retina and not in front of it

 The Far Point and Short-sightedness

• Remember that a "normal-sighted" person has a far point at infinity
  • A short-sighted person, however, has a far point that is less than infinity
• So choosing the correct diverging lens depends on the position of the far point for that person
  • The lens must have its principal focus in the same position as the eye's faulty far point

A Ray Diagram Showing the Far Point of the Eye and the Focal Length of the Lens

The focal length of the correcting lens is the same as the principal focus at the uncorrected far point of the eye

Long-sightedness

• Long-sightedness is also called hyperopia
• It happens when the lens is less curved than normal or the eyeball is too short
  • So the cornea and lens are too weak
  • Hyperopia can also occur if the eyeball is too short
• This means light rays are not refracted enough and so the focal point of the image falls behind the retina (rather than on it)
  • So close objects appear blurry because people with long-sightedness are unable to focus on near objects

Ray Diagram of Long-Sightedness

An eye that is long-sighted has a narrower lens with a smaller focussing power so the light rays meet and form an image behind the retina and not on it

Treatment of Long-sightedness

• Long-sightedness can be corrected using contact lenses or glasses with a converging (convex) lens
  • The lens causes the light rays to converge before reaching the eye
  • So when they are focussed by the eye the image now forms on the retina
• Remember from 10.1.1 Converging & Diverging Lenses that
  • Virtual images have a negative distance to the lens, v 
  • But the lens has a positive power
• A long-sighted person may need to wear glasses for reading but might remove them when driving because they can easily focus on objects far away from the eye

The Effect of a Diverging Lens on a Long-sighted Eye

The converging lens causes the rays to converge before they reach the eye, so the image is formed on the retina and not behind it

The Near Point and Long-Sightedness

• Remember that a "normal-sighted" person has a near point at around 25 cm 
  • A long-sighted person, however, has a near point which is further than this
• So choosing the correct converging lens depends upon the position of the near point for that person
  • The lens must produce a virtual image of objects that are 25 cm away at the eyes uncorrected near point

A Ray Diagram Showing the Uncorrected Near Point of an Objected at 25 cm

A virtual image of the object is formed at the uncorrected near point of the eye

Astigmatism

• The shape of the cornea is often assumed to be a perfect sphere, like a tennis ball
• People with astigmatism have eyes with irregularly shaped corneas, like an egg or a rugby ball

The Difference Between Perfect Spheres and Irregularly Shaped Corneas

The tennis ball represents a cornea that is a perfect sphere and non-astigmatic whereas the rugby ball represents a cornea that is irregular and astigmatic

• People with an irregularly shaped cornea have different focal lengths for different planes of vision
  • For example, when vertical lines are in focus then horizontal lines might not be
  • This is because light rays from each plane will come together at a different point 
  • These planes of vision can occur at any angle
    • It depends on the angle of the curvature of the cornea

The Structure of a Bridge Seen By Someone with Astigmatism and Someone Without

Someone with astigmatism struggles to focus horizontal and vertical lines at the same time

Comparison of Light Rays Brought Together for Astigmatic and Non-Astigmatic Eyes

In an eye with a spherically shaped cornea, the light rays come to the same point of focus at the retina. In an astigmatic eye, the light rays come together at different points of focus. 

Correcting for an Astigmatism

• Astigmatism can be corrected with a cylindrical lens that adds power to rays of light coming from one plane but not the plane perpendicular to it

An Example of a Cylindrical Lens Adding Power to One Plane of Light

The cylindrical lens brings light rays in the horizontal plane to a focus but does not affect the light rays in the perpendicular vertical plane

• There are many different combinations of astigmatism
• A few examples are:
  • One plane is short-sighted and the other long-sighted
  • One plane has correct vision and the is other long-sighted
  • Both planes are short-sighted by different amounts
• The cylindrical power (CYL) of the astigmatism is related to the difference in power between the two points of focus of the two planes of light
  • The greater the difference then the greater the astigmatism 
  • The smaller the difference then the smaller the astigmatism
  • It is measured in Dioptres (D)

The Cylindrical Power of the Astigmatism

The difference between the points of focus for the two planes of light is related to the cylindrical power of the astigmatism

• The astigmatism can be present at any angle on the curvature of the eye known as the angle of astigmatism 
  • This is measured in the same way as if a protractor is placed against the front of the eye
  • It is an angle measured from the left-hand side of the protractor between 0° and 180°

Angle of Astigmatism

The axis of astigmatism in the eye is found using the angle of the plane of the curved area of the eye. It is the curved area of the cornea that causes astigmatism. In this example, it is 155°.

Prescription for Astigmatism

• The prescription for the cylindrical lens to correct astigmatism will state the following three pieces of information for each eye:
  1. The sphere (SPH) - The focal power needed to correct for either long or short-sightedness 
  2. The cylinder (CYL) - The cylindrical power needed to correct for the astigmatism
  3. The axis angle - This is the angle needed by the lens to correct for astigmatism

An Example Astigmatism Prescription

The astigmatism prescription shows the sphere focal power, cylindrical power and axis angle

• In your exam, you may be asked to calculate the power of the lens needed in a prescription
• This is calculated for each eye by subtracting CYL from SPH
  • For example, in the image for the left eye this is +2.50 − 1.00 = 1.50 D
  • In the right eye this is +1.75 − 1.50 = 0.25 D
• Remember that one or both of the SPH and CYL values can be negative depending on the vision defect
  • So, you may need to subtract a negative power
  • e.g. +1.50 − − 0.50 = 1.50 + 0.50 = 2.00 D
• It is important to note that the angle of astigmatism and the axis angle for the prescription are perpendicular to each other
  • A curved area on the cornea at a specific angle causes astigmatism 
  • This is corrected by an equally curved area in the correcting lens placed perpendicular to it 

Angle of Astigmatism vs Axis Angle for Prescription

The diagram shows that the axis angle for the correcting lens must be perpendicular to the angle of astigmatism. The angle of astigmatism in this example is 155°, so the axis angle is 155 − 90 = 65°