Image Formation by Convex Mirror – Rankers Physics
Topic: Ray Optics
Subtopic: Lens Makers Formula/ Len's Formula

Image Formation by Convex Mirror

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

Solution:

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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