Final answer:
The expression for the equivalent focal length of a combination of two thin convex lenses in contact is given by the lens maker's equation: 1/f = (n-1)((1/R1) - (1/R2)), where f is the equivalent focal length, n is the refractive index, R1 is the radius of curvature of the first lens, and R2 is the radius of curvature of the second lens.
Step-by-step explanation:
To derive an expression for the equivalent focal length of a combination of two thin convex lenses in contact, we can use the lens maker's equation. According to the lens maker's equation, the inverse of the focal length of a lens is equal to the difference of the refractive indices of the lens material and the surrounding medium, multiplied by the sum of the curvature radii:
1/f = (n - 1)((1/R1) - (1/R2))
where f is the equivalent focal length of the combination of lenses, n is the refractive index of the lens material, R1 is the radius of curvature of the first lens, and R2 is the radius of curvature of the second lens.