One in the Eye

The eye is a sophisticated organ.  Without it we cannot do many things that we take for granted.  Without your eyes you cannot read this text here.  Its structure is this:

Cataracts are a common problem for older people.  The eyesight deteriorates and blindness can follow.  However it is possible to correct it with a short operation where the old lens is removed and an implant inserted.

Contact lenses are used to correct defects of vision.  They are more sophisticated nowadays and allow oxygen to pass to the cornea (which does not have a separate blood supply).

Light from an object enters the eye through the cornea. The curved cornea and the lens produce an image on the retina.   There are several boundaries at which refraction takes place.  However the main refraction takes place at the air cornea boundary, not the lens, which does the fine focusing.

The image is upside down on the retina as shown:

The eye has a system of muscles called ciliary muscles that alter the shape of the lens.  If you look at a close-up object the lens fattens, becoming optically stronger.  If you look at a distance object the muscles relax and the lens goes thinner.

The ciliary muscles enable the eye to accommodate, i.e. adjusting to closer or further objects.  The closest you can accommodate is about 10 cm when you are young.  This lengthens with age so that at 75, you might not be able to accommodate to objects closer than 1 metre.

Convex Lens

Lenses work by refracting light at a glass-air boundary.  Although refraction occurs at the boundary, we will treat all lenses as bending the rays at the lens axis.

The lens in the eye is a convex or converging lens.  This means that the lens makes rays of light come together, or converge.

The rays parallel to the principal axis are converged onto the principal focus.  The focal length is the distance between the lens axis and the principal focus (strictly speaking, the focal plane).

Thicker lenses bend light more, and are therefore described as more powerful.  Powerful lenses have short focal lengths.  The power of a lens is measured in dioptres (D) and is given by the formula:

Power =          1               

               focal length (m)

The principal focus of a convex lens is called real.  The images made by convex lenses are in most cases real.  This means that the image can be projected onto a screen. 

Lens powers add up so:

Ptot = P1 + P2 + ...

Concave Lens

The concave lens splits rays parallel to the principal axis, which is why it is called a diverging lens.

The principal focus is virtual because the rays do not pass through it , but diverge as if they had come from it.  Images in concave lenses are always virtual because they cannot be projected onto a screen.

The power of a concave lens is always negative, for example -1.5 D.

Ray Diagrams

We can determine where an image lies in relation to the objects by using a ray diagram.  We can do this by using two simple rules:

• Draw a ray from the top of the image parallel to the principal axis.  This ray bends at the lens axis and goes through the principal focus.

• Draw a ray from the top of the lens through the centre of the lens.

Where the two rays meet, that is where the image is found.  The diagrams shows how we do a ray diagram step-by-step:

Step 1:  Draw the ray parallel to the principal axis.

Step 2: Draw the refracted ray so that it passes through the principal focus.

Step 3: Draw a ray from the top of the object through the middle of the lens.  This ray is un-deviated.

Step 4:  Where the rays meet, that is where the image is.

It is a good idea to draw your ray diagrams on graph paper as the following ray diagrams are.  Be careful with your drawing; a small change in the angle of the un-deviated ray can lead to quite a big change in the final position of the image.  And PLEASE... Be a good chap and use a sharp pencil.

This ray diagram is done on graph paper:

This diagram shows where an object is at a distance of greater than twice the focal length.  The image is inverted (upside down), real, and diminished (smaller).

What is the image like if the object is at 2F? 

What is the image like if the object is between 2F and F? 

What is the image like if the object is at F? 

What is the image like if the object is less than F? 

For a concave lens, the process is similar, except that we extend the refracted parallel ray back to the virtual principal focus.

The Lens Formula

Lens diagrams have the main disadvantage that there is uncertainty in precisely where the image is.  Therefore the use of the lens formula is better.  The lens formula is:

[f - focal length; u - object distance; v - image distance]

If you are going to use dioptres you must work in metres.  The convention for the equation is that real is positive.  For a concave lens, the focal length is negative, because the principal focus is virtual.  If the image position gives a negative value, then the image is virtual. 

Optical properties

Glass is good at transmitting light, but about 10 % gets reflected.  We can add a coating that reduces this, by being thick enough to cause a path difference of 1/2 a wavelength.  The waves superpose and cancel out, because they are p radians out of phase.

Ultra-violet light can be damaging to eye-sight.  Some tinted coatings can reduce the transmittance of UV light to reduce the harmful radiation.

Vision Under Water

If you dive under water, your vision is blurred.  This is because the eye is designed to work in air, with refractive index 1.0.  Water has a refractive index of about 1.33, and the refractive index of the cornea is not much different.  So the rays are hardly deviated on passing the boundary.

• Water birds have much greater accommodation; the lens can go much fatter.

• A diver wears a mask with a flat sheet of glass or plastic.  This enables there to be an air-cornea boundary.

When dealing with problems like this, use Snell's Law:

    n1sinq1 = n2sinq2