Question

Consider a lens made to the following specifications: focal length for red light fred=19.57cm, focal length for blue light fblue=18.87cm. Consider an object 5.000cm tall placed a distance 30.00cm from the lens. Assuming that the object reflects both red and blue light, find the ratio yredyblueof the height of the red image to the height of the blue image.

Answer 1

fred = 19.57 cm

let the image and object distance be u and vred

1/fred = 1/vred - 1/u

1/19.57 = 1/vred + 1/30

vred = 56.29 cm

magnification = hired/ho = - vred/u

hired = - 5*56.29/30

hired = - 9.38 cm

fblue = 18.87 cm

let the image and object distance be u and vblue

1/fblue = 1/vblue - 1/u

1/18.87 = 1/vblue + 1/30

vblue = 50.86 cm

magnification = hiblue/ho = - vblue/u

hiblue = - 5*50.86/30

hiblue = - 8.48 cm

let ratio of the height of the red image to the height of the blue image.be Y

Y = hired / hiblue = -9.38/-8.48

Y = 1.11