Efficiency of a convex lens When the intensity of a light source is measured before and after the light passes through a convex lens, should the two intensity values theoretically be the same? In other words, can a convex lens capture and transmit all photons incident on it by altering their paths only? Or is the ability of a convex lens to capture light dependent on the characteristics of the light (e.g. frequency)?
I haven't been able to find clear answers to this question.
Thank you.
 A: In theory yes, but in practice no.

*

*A lens is a refractive element, so there will alway be some Fresnel reflection which will reduce the transmitted intensity


*The len’s material is not perfectly transparent, some intensity will be lost by absorption


*Surfaces are not perfect and will scatter some intensity out of the beam
The transmission efficiency of a lens is,
$$
T = 1 - R - S - A
$$
where $R$ is the fraction reflected, $A$ is the absorptivity of the lens, and $S$ is the fraction scattered out of the beam by volume or surface scattering events.
You can make some estimates for refractive index of $n=$1.5, absorption coefficient of $\alpha=$0.02cm$^{-1}$ and thickness of $d=$1cm.
$$ 
T \approx 1 - 2\left( \frac{n-1}{n+1} \right)^2 - \left( 1 -  e^{-\alpha d}\right)
$$

*

*The second term assumes two normal incidence reflections but just applies the reduction globally rather than sequential as would be the case

*The third term is the Beer Lambert law using sensible values for transparent materials.

$$
T \approx 1 - 0.08 - 0.02 \approx 0.9
$$
