Lens maker's formula is applicable to

Options

A. Thin lenses and paraxial rays which subtend very small angles with the principal axis
B. Thick lenses and paraxial rays which subtend very small angels with the principles axis
C. Thin lenses and for marginal rays
D. Thick lenses and for marginal rays

Answer

### Step-by-Step Solution:

1. **Understanding the Lensmaker's Formula**:
The Lensmaker's formula relates the focal length of a lens to the radii of curvature of its surfaces and the refractive index of the lens material. It is given by the formula:
\[ \frac{1}{f} = \left( n - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
where \( f \) is the focal length, \( n \) is the refractive index, and \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces.

2. **Identifying Lens Types**:
The Lensmaker's formula is primarily applicable to thin lenses. A thin lens is defined as one where the thickness of the lens is negligible compared to the radii of curvature of its surfaces and the focal length.

3. **Considering Ray Types**:
The formula is also applicable when considering paraxial rays. Paraxial rays are those that make small angles with the optical axis and are close to it. These rays can be approximated well by the lensmaker's formula.

4. **Excluding Other Options**:
- Thick lenses: The Lensmaker's formula does not hold for thick lenses because the thickness becomes comparable to the focal length, and the assumptions made in deriving the formula do not apply.
- Marginal rays: Marginal rays are those that are farther from the optical axis and do not converge at a single focal point like paraxial rays do. The lensmaker's formula does not apply to these rays.

5. **Conclusion**:
Therefore, the Lensmaker's formula is applicable to thin lenses and paraxial rays. The correct answer is that the formula applies to thin lenses and paraxial rays.

### Final Answer:
The Lensmaker's formula is applicable to **thin lenses and paraxial rays**.

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