Validity of Spherical Mirror Formula and Laws of Reflection

To determine the correct option, let us analyze both statements individually based on the principles of geometrical optics.

Analysis of Statement-1:

The spherical mirror formula is given by:
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

This formula is derived under the paraxial ray approximation, which assumes that:

1. All rays make very small angles with the principal axis ($\sin\theta \approx \tan\theta \approx \theta$).
2. The aperture (linear size) of the mirror is very small compared to its radius of curvature $R$.

For a spherical mirror with a large aperture, marginal rays (rays striking near the edges) and paraxial rays (rays striking near the pole) do not converge at a single focal point, leading to an optical defect known as spherical aberration. Therefore, the relation connecting $u, v,$ and $f$ holds accurately only for mirrors whose sizes are very small compared to their radii of curvature.

Thus, Statement-1 is True.

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Analysis of Statement-2:

The laws of reflection state that:

1. The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
2. The angle of incidence $i$ is equal to the angle of reflection $r$ ($i = r$).

These laws are fundamental principles of physics and hold strictly for all reflecting surfaces (whether plane, spherical, cylindrical, small, or large) at any local point of incidence. For a spherical surface, the normal at any point is simply the radius vector connecting that point to the center of curvature $C$.

Therefore, the statement claiming that laws of reflection are not valid for large spherical surfaces is incorrect.

Thus, Statement-2 is False.

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Conclusion:

• Statement-1 is True.
• Statement-2 is False.

Hence, the correct choice is (C).