Mirror Formula Validity – Rankers Physics

Reflection by Spherical Mirrors: Practice Problem & Solution

Assertion (A): The formula \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) connecting u and v for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvatures. Reason (R): Laws of reflection are strictly valid for smaller size of optical system.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Reflection by Spherical Mirrors. Understanding the underlying formula is key to arriving at the correct answer below:

Mirror formula \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) is valid under paraxial approximation, which requires small aperture mirrors. Laws of reflection are fundamental, and their simplified application in the mirror formula relies on paraxial rays. Thus, both (A) and (R) are true, and (R) correctly explains (A).

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