Question

Two lenses made of kinds of glass having different refractive indices n1=1.55 and n2=1.47 are cemented together to form what is called an optical doublet. Optical doublets are often used to correct chromatic aberration in optical devices. The first lens of a doublet has one flat side and one concave side if radius of curvature12cm . The second lens has two convex sides of radius of curvature 12cm. Find the focal length of this optical doublet.

Answer 1

Optical doublets are used to correct chromatic aberration caused by the different refraction of light with different wavelengths. In this case, the optical doublet is made up of two lenses with different refractive indices and curvatures. However, when the values are plugged into the lens maker's formula, there is no valid solution for the focal length of the optical doublet.

Step-by-step explanation:

Chromatic aberration occurs due to the fact that the index of refraction of a lens depends on the wavelength of light. This means that light of different wavelengths will focus at different points, resulting in colored and blurred edges in an image. Optical doublets, which are formed by cementing two lenses together, can correct chromatic aberration by combining lenses made of different materials and with different dispersions. In this case, the optical doublet consists of a lens with a flat side and a concave side, and a lens with two convex sides, both with a radius of curvature of 12cm. To find the focal length of this optical doublet, we can use the lens maker's formula:

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

where f is the focal length, n is the refractive index, and R1 and R2 are the radii of curvature for each lens. Plugging in the values, we get:

1/f = (1.55 - 1) * (1/12 - 1/12)

1/f = 0.55 * 0

1/f = 0

Since the equation becomes 0 = 0, there is no valid solution for the focal length of this optical doublet.