# Activity: Resolution

#### Aims

- Measure the resolution of the eye.
- Understand the meaning of resolution.
- Understand how diffraction affects resolution.
- Apply the Rayleigh criteria to solve problems of resolution.

#### How the eye works

Light from a point source passes into the eye through the pupil, is focused by the lens onto the retina where light sensitive cells detect the light and send information to the brain via the optic nerve.

#### The resolving power of the eye

The resolving power of the eye is its ability to see detail in an image. This can be tested by looking at the two dots in the centre of the square below.

If your screen is set to show the image at 100% the distance between the dots is 1mm, measure with a ruler to be sure.

When looking at two dots point images will be formed on the retina.

- Move way from the screen until you can't resolve the two dots (they look like one dot).
- Measure the distance from your eyes to the screen.

The light from the dots subtends an angle to the eye as illustrated below.

- Calculate the angle subtended by the dots to the eye.
- If the dots were 5mm apart what is the maximum distance at which they could be resolved?

#### Diffraction at the eye

When light passes through the pupil (the aperture that allows light to pass into the eye) it diffracts in the same way as when light passes through a narrow slit except that the diffraction is in 2 dimensions. The result is a circle in the centre with rings around the outside.

The equation for the position of the first minima is

Where b is the diameter of the aperture.

Note that if the angle is small and measured in radians

- Is the pattern more spread out or narrower than the single slit diffraction pattern for a slit width b?
- Can you explain why this might be the case?
- If the pupil has a diameter of 5mm calculate the angle, θ to the first minimum for light of wavelength 600 nm.

When the light from the two dots arrives at the retina it is spread out. If the two dots are too close the two circles of light will overlap making them look like one. This can be shown in the animation below showing how the image on the retina would change if the dots were moved closer (then further away).

#### Rayleigh Criterion

The Rayleigh criterion gives the condition for two point sources to be resolved:

Two points are resolved if the principal maxima of one diffraction pattern coincides with the first minima of the other.

So if the image of the second dot is such that its principal maxima is coincident with the 1st minima of the first one it will just be resolved.

We can use this to predict the maximum distance from the eye that two 1mm apart dots can be resolved.

- What is the value of angle θ for the eye (you just calculated it).
- This is the same as the angle subtended by the dots to the eye, use the angle to calculate the distance between the eye and the dots when they are just resolvable according to the Rayleigh criterion.
- Does this agree with your experimental value?
- OK, the values aren't the same, why not?

This principle applies to all optical instruments (camera, telescope etc.)

- How could you increase the resolving power of an optical instrument?
- It is claimed that it might be possible to read newspaper print from a satellite. Comment on this claim.
- Why do electron microscopes use electrons?