# Imaging aberration

Qs: Doesn't a curved side lens produce less aberration than a flat lens in general because the overall angle of deviation is smaller in the curved lens?

Consider the following experimental results for the image resolution due to each geometry:

It follows that the resolution $$L_{curve}>L_{flat}$$.

However this was unexpected because for spherical/parabolic lenses, spherical aberration is related to the angle of deviation via the approximate relation: $$abberation \approx \delta ^3$$ (derived from the fact that $$sin(x)=x-x^3/3!+....$$ and $$\delta=angle_{in}-angle_{out}$$ and deviation from Snell's law).

Implying that

for (a)(flat) & (b)(curve) $$abberation_{flat} \approx \delta^3$$

$$abberation_{curve} \approx 2\left(\frac{\delta}{2}\right)^3=\frac{\delta^3}{4}$$

Thus, assuming the resolution decreases with aberration, a curveside lens is expected to yield a higher resolution $$L$$, which contradicts with my experimental results (and I'm fairly confident that the results were correct as repeated readings were used).

The same conclusion was reached for the doublet lenses which were used to reduce chromatic aberration.

A resolution test chart & CMOS camera were used to determine the experimental resolution

What am I missing? why did the experimental results not agree with the theory?