# Homework Help: Chromatic aberration question

1. Feb 22, 2005

### StonieJ

Essentially, I'm curious as to why the focal length of a lens with red light is the closest to the focal length in white light.

According to the lens-maker's equation, the focal length of a lens depends on the index of refraction of the lens material, which in turn is dependent upon the wavelength of the light being used. By observing the dispersion curve for a given lens, one can see that as the wavelengths get longer (towards red), the dispersion curve levels off (gets less negatively steep), indicating that the index of refraction for red is small and therefore red light is not highly bent as it passes through the lens. Blue light, on the other hand, has a high index of refraction and is focused to a point in front of the red light focal length.

Does that look right up to this point? I hope so, but I still don't feel like I'm answering the fundamental question of why red light is closest to white light. I'm just describing why it is refracted less than blue light (and I may not even be doing a good job of that). If white light contains both red and blue, then why does it more closely resemble that of red, and not something in between the two?

2. Feb 22, 2005

### vincentchan

3. Feb 22, 2005

### StonieJ

Here is the actual question:

"Compare the focal lengths of lens B (focal length 16.0 +/- 0.2 cm) for white, red, green, and blue light. For which of the three colors is the focal length more nearly the same as for white light? Explain."

My data is:
white = 15.9 cm
red = 15.7 cm
green = 15.6 cm
blue = 15.2 cm

Maybe by "explain" they don't mean "tell us why the focal length for red light is closest to white light" but that's the impression I got.

Thanks.

Last edited: Feb 22, 2005