Question

When the object is placed at 2F (centre of curvature) in front of a concave mirror then its image is formed at :

• A. 2F
• B. F
• C. infinity
• D. between F and 2F

Hint:

For a concave mirror:
Object at \(\infty\) \(\rightarrow\) Image at F
Object beyond 2F \(\rightarrow\) Image between F and 2F
{Object at 2F (Center of Curvature, C) \(\rightarrow\) Image at 2F (C)}
Object between F and 2F \(\rightarrow\) Image beyond 2F
Object at F \(\rightarrow\) Image at \(\infty\)
Object between P and F \(\rightarrow\) Image behind mirror The image formed when the object is at 2F is real, inverted, and the same size as the object.

Answer 1

The Correct Option is A

Concept: For a spherical mirror, the center of curvature (C) is at a distance of twice the focal length (F) from the pole of the mirror. So, 2F is equivalent to the center of curvature C. The position of the image formed by a concave mirror depends on the position of the object. Case: Object at the Center of Curvature (C or 2F) of a Concave Mirror When an object is placed at the center of curvature (C, which is at a distance 2F from the pole) of a concave mirror:
Position of the image: The image is also formed at the center of curvature (C or 2F).
Nature of the image: The image is real (can be formed on a screen) and inverted.
Size of the image: The image is the same size as the object (magnification \(m=-1\), where the negative sign indicates inversion). Analyzing the options:
(1) 2F: Correct. The image is formed at 2F (the center of curvature).
(2) F: The image is formed at F when the object is at infinity.
(3) infinity: The image is formed at infinity when the object is at F.
(4) between F and 2F: The image is formed between F and 2F when the object is beyond 2F. Therefore, when the object is placed at 2F in front of a concave mirror, its image is formed at 2F.