Direction: In the following questions, a statement of assertion (A) i...
Assertion and Reasoning
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 above given system, the equation 1/u 1/v = 1/f gives v = ∞
Explanation
Convex mirrors are curved mirrors that reflect light outwards. They have a virtual focus and a positive focal length. When an object is placed in front of a convex mirror, the image formed is always virtual, erect, and diminished.
The given assertion states that a point object is placed at a distance of 26 cm from a convex mirror of focal length 26 cm. In this case, the object distance u is equal to the focal length f, which means that the image distance v is also equal to the focal length. Therefore, the image formed is at a distance of 26 cm from the mirror.
The given reasoning states that for the above system, the equation 1/u 1/v = 1/f gives v = ∞. This is not correct as the object distance u is equal to the focal length f, and the equation becomes 1/u + 1/v = 1/f. Rearranging this equation, we get v = uf/(u-f) = 26 cm, which means that the image is formed at a finite distance from the mirror and not at infinity.
Therefore, the assertion is true as the image is not formed at infinity, but the reasoning is false as it does not correctly explain the assertion. Hence, the correct option is (C) Assertion (A) is true but reason (R) is false.
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