PX284 - T6 - images

real image

note: image is inverted
height of image / height of object:

\frac{θ v}{θ u} = \frac{v}{u}

from thin lens equation:

\frac{v}{u} = \frac{1}{u} (\frac{f u}{u - f}) = \frac{f}{u - f}

assuming $u ≫ f :$

\frac{v}{u} ≃ \frac{f}{u}

the image is inverted

virtual image

here, $u < f :$

\frac{1}{v} = \frac{1}{f} - \frac{1}{u} < 0

height of image $>$ height of object, and the image is not inverted

\frac{θ v}{θ u} = \frac{v}{u} < 0

limits of resolution:
- quality of lenses
- diffraction (wave nature of light)
- ability to resolve small angles
  - for the eye: $θ_{m i n} \sim 3 \times 10^{- 4}$ radians
to overcome the angular resolution, make the distance shorter, until the limit of 'near point', $d_{N P}$

for $d < d_{N P}$ , eye cannot become stronger, so image behind retina
without magnifying glass:

θ_{m i n} = \frac{l}{d_{N P}}

magnification:

M = \frac{d_{N p}}{f}

eg: for $f \sim 2.5$ cm, $M \sim 10$