A parallel beam of light falls on a concave mirror of focal length 12 cm. To determine the nature and the position of the image, a student executes the following steps. Arrange them in the correct order.
(A) Uses the mirror formula \( \displaystyle\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \) with \( u = -\infty \)
(B) Concludes whether the image is real or virtual from the sign of image distance v.
(C) Draws the ray diagram showing rays parallel to the principal axis passing through focus after reflection.
(D) Determines the image distance v.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (C), (A), (D), (B)
The steps follow the logical route of solving an optics problem: first the ray diagram to see where the image forms, then the mirror formula to find the image distance, and finally the sign of v to decide the nature of the image.
(C) Draws the ray diagram showing rays parallel to the principal axis passing through focus after reflection. — The ray diagram comes first: rays parallel to the principal axis pass through the focus after reflection, so the image is expected at F.
(A) Uses the mirror formula \( \displaystyle\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \) with \( u = -\infty \) — A parallel beam comes from an object at infinity, so \( u = -\infty \) is used in the mirror formula. With the Cartesian sign convention, f = −12 cm for a concave mirror.
\( \displaystyle \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-12} - 0 \)
(D) Determines the image distance v. — The image distance follows:
\( v = -12\,\mathrm{cm} \)
(B) Concludes whether the image is real or virtual from the sign of image distance v. — v is negative, so the image is formed in front of the mirror, where the reflected rays actually meet: the image is real (a point image at the focus).
So the correct order is (C), (A), (D), (B).