Using the section on Lens Aberrations and the Supplemental Optics section in the

Question

Using the section on Lens Aberrations and the Supplemental Optics section in the Biomedical Physics textbook answer the questions below. The following table gives the indices of refraction for crown glass and flint glass according to wavelength of light:* Correcting lens aberrations is a difficult task due to the precision required. Chromatic aberration can be corrected in part by coupling a converging lens with a diverging one. Although the focal points of red light and blue light are separated by a converging lens because of dispersion, adding a diverging lens (which must have a different index of refraction) to the system bends light in the opposite direction. It is possible, therefore, to combine some of the wavelengths of light at one focal point by adjusting the index of refraction of the lenses and their curvatures. Find the the magnitude of the separation between the focal length for blue light and the focal length for red light for a double convex lens made of crown glass with a left radius of +6 cm and a right radius of -6 cm (note that the negative sign indicates the direction of curvature assuming the left-to-right direction is positive). Keep two decimal places in your answer.

Explanation / Answer

use lense makers formula,

1/f = (n - 1)*(1/R1 - 1/R2)

given

n_blue = 1.5293

n_red = 1.5204

R1 = 6 cm

R2 = -6 cm

1/f_blue = (n_blue - 1)*(1/R1 - 1/R2)

= (1.5293 - 1)*(1/6 - 1/(-6))

f_blue = 5.67 cm

1/f_Red = (n_Red - 1)*(1/R1 - 1/R2)

= (1.5204 - 1)*(1/6 - 1/(-6))

f_Red = 5.76 cm

so, f_Red - f_blue = 5.76 - 5.67

= 0.09 cm

= 0.9 mm

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