WILL RATE LIFESAVER PLEASE SHOW WORK Chromic abberations are the result of an in

Question

WILL RATE LIFESAVER PLEASE SHOW WORK

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 17.04 cm and is 17.09 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 55 mm high object is placed 64 cm from the lens. Where is the blue image formed? Tries 0/10 Where is the red image formed? Tries 0/10 How big is the red image? Tries 0/10 How big is the blue image?

Explanation / Answer

Part A)

For the blue

1/f = 1/p + 1/q

1/17.09 = 1/64 + 1/q

q = 23.32 cm

Part B)

For the red

1/17.04 = 1/64 + 1/q

q = 23.22 cm

Part C)

Red image size

h'/h = -q/p

h'/55 = -23.33/64

h' = -19.96 mm (negative means its inverted - ignore it if needed)

Part D)

Blue size image

h'/55 = -23.32/64

h' = -20.04 mm (again, negative means its inverted - ignore it if needed)

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