Question

Chromatic aberration comes from the fact that different wavelengths of light travel at different speeds through the material of the lens; that is, they have different indices of refraction, a property known as dispersion. This means that a lens, in effect, has different focal lengths for different wavelengths of light. Consider a lens made to the following specifications: focal length for red light fred=19.57cm, focal length for blue light fblue=18.87cm.

Part A

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.

Express your answer numerically to three significant figures.

Answer 1

y_red / y_blue = 1.11

Step-by-step explanation:

Let's use the constructor equation to find the image for each wavelength

1 /f = 1 /o + 1 /i

Where f is the focal length, or the distance to the object and i the distance to the image

Red light

1 / i = 1 / f - 1 / o

1 / i_red = 1 / f_red - 1 / o

1 / i_red = 1 / 19.57 - 1/30

1 / i_red = 1,776 10-2

i_red = 56.29 cm

Blue light

1 / i_blue = 1 / f_blue - 1 / o

1 / i_blue = 1 / 18.87 - 1/30

1 / i_blue = 1,966 10-2

i_blue = 50.863 cm

Now let's use the magnification ratio

m = y ’/ h = - i / o

y ’= - h i / o

Red Light

y_red ’= - 5 56.29 / 30

y_red ’= - 9.3816 cm

Light blue

y_blue ’= 5 50,863 / 30

y_blue ’= - 8.47716 cm

The ratio of the height of the two images is

y_red ’/ y_blue’ = 9.3816 / 8.47716

y_red / y_blue = 1,107

y_red / y_blue = 1.11