A double concave lens made of flint glass is placed next to the converging lens

Question

A double concave lens made of flint glass is placed next to the converging lens described above. In order to reduce the separation between the red and blue focal points, the double concave lens must have radii near -17 cm and +17 cm. The focal length for red light with the diverging lens by itself is -11.9214 cm; for blue light the focal length is -11.5207 cm. If the two lenses are in contact, what is the magnitude of the resulting difference between the focal point for red light and the focal point for blue light? Again, keep two decimal places in your answer. answer in mm.

The following table gives the indices of refraction for crown glass and flint glass according to wavelength of light: color blue yellow red crown glass (n) 1.5293 1.5230 1.5204 flint glass (n) 1.7378 1.7200 1.7130 wavelength (nm) -486 -589 -656

Explanation / Answer

If the two lenses are in contact, then the resulting difference between the focal point for red light and the focal point for blue light which will be given as :

using a formula, we have

1 / f = 1 / fred + 1 / fblue

In converging lens, focal length is positive.

1 / f = 1 / (11.9214 cm) + 1 / (11.5207 cm)

1 / f = 0.170683 cm

f = 5.85 cm

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