Assertion : A point object is placed at a dis | vedclass

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(C) For a convex mirror,the focal length $f$ is taken as positive $(f = +26 \ cm)$. The object distance $u$ is always taken as negative $(u = -26 \ cm

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If the Assertion is correct but Reason is incorrect.

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(C) For a convex mirror,the focal length $f$ is taken as positive $(f = +26 \ cm)$. The object distance $u$ is always taken as negative $(u = -26 \ cm)$.Using the mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.Substituting the values: $\frac{1}{v} + \frac{1}{-26} = \frac{1}{26}$.$\frac{1}{v} = \frac{1}{26} + \frac{1}{26} = \frac{2}{26} = \frac{1}{13}$.Thus,$v = +13 \ cm$.The image is formed at $13 \ cm$ behind the mirror,not at infinity. Therefore,the Assertion is correct.The Reason states that the equation gives $v = \infty$,which is mathematically incorrect based on the sign convention. Thus,the Reason is incorrect.

Assertion : $A$ point object is placed at a distance of $26 \ cm$ from a convex mirror of focal length $26 \ cm$. The image will not form at infinity.
Reason : For the above-given system,the equation $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ gives $v = \infty$.

Similar Questions

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Assertion : $A$ point object is placed at a distance of $26 \ cm$ from a convex mirror of focal length $26 \ cm$. The image will not form at infinity.Reason : For the above-given system,the equation $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ gives $v = \infty$.