HELPP Chromic abberations are the result of an index of refraction that varies w

Question

HELPP

Chromic abberations are the result of an index of refraction that varies with the color of the light. This variation in the index of refraction results in a different focal length for different colors.
Consider the situtation in which the focal length of a particular lens is for red light is 24.05 cm and is 24.1 cm for blue light. That small difference in focal lenghts will have a small impact on the location and size of the images formed.
It also means that the red image will be out of focus at the location where the blue image is in focus, and vice versa.
For this problem, consider a 59 mm high object is placed 73 cm from the lens.

Where is the blue image formed?

Where is the red image formed?

How big is the red image?

How big is the blue image?

Explanation / Answer

For the blue image

1/f = 1/p + 1/q

1/ 24.1 = 1/73 + 1/q

q = 35.98 cm

For the red image

1/24.05 = 1/73 + 1/q

q = 35.87 cm

Size of red image

h'/59 = -35.87/73

h' = -28.99 mm (negative means inverted - ignore it if needed)

Size of blue image

h'/59 = 35.98/73

h' = -29.08 mm (same idea with the negative)

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