Chromatic Aberration in a Thin Convex Lens

Chromatic aberration is a phenomenon that occurs when a lens fails to focus different colors of light at the same point. This results in a blurred or distorted image. In the case of a thin convex lens, chromatic aberration can be calculated using the refractive index and radii of curvature.

Refractive Index of Flint Glass

The refractive index of a material determines how much light is bent or refracted when it passes through the material. In the case of flint glass, the refractive index varies from 1.60 to 1.66 for the visible range. This means that light of different colors will experience different amounts of refraction when passing through the lens.

Radii of Curvature

The radii of curvature of a lens determine its shape and curvature. In this case, the thin convex lens has a radius of curvature of 10 cm on one side and 15 cm on the other side. The difference in radii of curvature indicates a difference in the lens thickness.

Calculating Chromatic Aberration

To calculate the chromatic aberration between extreme colors, we need to consider the difference in refractive index and the lens thickness. Here's how we can do it:

1. Calculate the refractive index difference:
- Δn = n_blue - n_red
- Δn = 1.66 - 1.60
- Δn = 0.06

2. Calculate the lens thickness difference:
- Δs = R2 - R1
- Δs = 15 cm - 10 cm
- Δs = 5 cm

3. Use the lens formula to calculate the chromatic aberration:
- ΔC = (Δn * Δs) / (n_avg * R1 * R2)
- n_avg = (n_blue + n_red) / 2
- n_avg = (1.66 + 1.60) / 2
- n_avg = 1.63

- ΔC = (0.06 * 5 cm) / (1.63 * 10 cm * 15 cm)
- ΔC = 0.0184 cm

Chromatic Aberration Calculation Result

The calculated chromatic aberration between extreme colors is 0.0184 cm. This means that when light passes through the thin convex lens, the extreme colors will be focused at slightly different points, causing a blur or distortion in the image. It is important to minimize chromatic aberration in optical systems by using lenses with lower dispersion or using corrective elements.

Note: The calculations provided here are based on the given information and assumptions. Actual optical systems may involve more complex calculations and considerations.