Image Formation by Convex Mirror – Rankers Physics

Lens Makers Formula/ Len's Formula: Practice Problem & Solution

Assertion (A): A point object is placed at a distance of \(26 \text{ cm}\) from a convex mirror of focal length \(26 \text{ cm}\). The image will form at infinity. Reason (R): For above given system the equation \(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\) gives position of image.  
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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Lens Makers Formula/ Len's Formula. Understanding the underlying formula is key to arriving at the correct answer below:

For a convex mirror, focal length \(f = +26 \text{ cm}\). Object distance \(u = -26 \text{ cm}\). Using mirror formula \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) gives \(\frac{1}{v} = \frac{1}{26} - \frac{1}{-26} = \frac{2}{26} = \frac{1}{13}\) so \(v = 13 \text{ cm}\). (A) is false. The correct mirror formula is \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) not \(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\). (R) is false. Thus, both (A) and (R) are false.

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