Question

State limitations of the formula for the refraction of light on a spherical surface: \[ \frac{n_1}{u} + \frac{n_2}{v} = \frac{n_2 - n_1}{R} \] where symbols have their usual meanings.

Hint:

Always apply this formula only for paraxial rays to avoid large errors.

Answer 1

Step 1: Understanding the formula.
The relation is derived using approximations under the paraxial condition (rays close to the principal axis).
Step 2: Limitations.
1. It is valid only for small angles of incidence, refraction, and aperture (paraxial rays).
2. It ignores aberrations such as spherical and chromatic aberrations.
3. It assumes the medium is homogeneous and isotropic.
4. It cannot be applied when light rays are far from the axis (large aperture system).
Step 3: Conclusion.
Hence, the formula is only approximate and fails for wide-angle rays or real optical systems with aberrations.