The Eye and Seeing: Quick Revision

A brief note on The Eye and Seeing. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• The cornea and the eye lens form a real, inverted, small image on the retina. The brain turns it upright.
• The iris sets the size of the pupil; the ciliary muscles change the shape of the lens.
• Accommodation: a thick lens for near objects, a thin lens for far ones.
• A normal eye sees clearly from its near point, about $25\ \text{cm}$, to its far point at infinity.
• Short sight: a concave lens with $f = -(\text{far point})$. Long sight: a convex lens that puts a page at $25\ \text{cm}$ at the near point.

The facts at a glance

A worked example

A woman's near point is $65\ \text{cm}$. What lens lets her read at $25\ \text{cm}$?

1. The distances. The page is at $u = -25\ \text{cm}$; its image must be at $v = -65\ \text{cm}$.
2. The power. $P = 100 \times \left(\dfrac{1}{25} - \dfrac{1}{65}\right)\ \text{D} = 4\ \text{D} - 1.54\ \text{D} = +2.46\ \text{D}$.
3. So she needs a convex lens of $+2.46\ \text{D}$.

Practice with new numbers

A program to try

The program finds the lens for a short-sighted and a long-sighted eye.

Mistakes to avoid

• 'The eye lens does most of the bending.' The cornea does; the lens fine-tunes.
• Giving a lens for short sight a positive power. It is concave, so negative.
• Using the far point for long sight. Long sight uses the near point and the page at $25\ \text{cm}$.
• Forgetting metres. $P = \dfrac{1}{f}$ needs $f$ in metres.

Check yourself

1. Which cells of the retina let us see colours?

2. A far point is $1.8\ \text{m}$ away. What lens corrects the eye?

3. Reading glasses of $+1.5\ \text{D}$ let a man read at $25\ \text{cm}$. Where is his near point?

4. A door $2\ \text{m}$ tall is $5\ \text{m}$ away. How tall is its image on the retina, $2.5\ \text{cm}$ behind the lens?