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Assertion (A): 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 (R): For above given system the equation 1f=1v+1u\dfrac{1}{\text f} = \dfrac{1}{\text v} + \dfrac{1}{\text u}​ gives v = ∞.

options

  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, and R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.

Reflection of Light

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Answer

A is true but R is false.

Reason —

Assertion (A) is true because For a convex mirror with f\text f = +26 cm and an object at u\text u = −26 cm (in front of the mirror), the mirror formula gives;

1f=1v+1u⇒126=1v+1−26⇒126=1v−126⇒1v=126+126⇒1v=226⇒v=262⇒v=+13 cm\dfrac{1}{\text f} = \dfrac{1}{\text v} + \dfrac{1}{\text u} \\[1em] \Rightarrow \dfrac{1}{26} = \dfrac{1}{\text v} + \dfrac{1}{-26} \\[1em] \Rightarrow \dfrac{1}{26} = \dfrac{1}{\text v} - \dfrac{1}{26} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{1}{26} + \dfrac{1}{26} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{2}{26} \\[1em] \Rightarrow \text v = \dfrac{26}{2} \\[1em] \Rightarrow \text v = +13 \text { cm}

Hence, the image is not at infinity.

Reason (R) is false because using the same formula does not give v = ∞.

Therefore, A is true but R is false.

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