PhysicsCBSE Class 12 · Board exam 2025, set 55/7/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2025: question 18(a)

Set in the CBSE Class 12 board exam of 2025, paper 55/7/1, section B, question 18(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q18(a) · 2 marks · Very short answerRay Optics and Optical Instruments

Using the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus."

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 55/7/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

For a convex mirror f is positive and u is always negative in the Cartesian sign convention.

Hint 2

Get 1/v from the mirror formula and compare it with 1/f; then write m = −v/u.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

For a convex mirror, take $f > 0$ (focus behind the mirror). For a real object, $u = - x$ with $x > 0$ . Mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} = \frac{1}{f} + \frac{1}{x}$ .
½ mark
Both terms on the right are positive, so $v > 0$ : the image is always behind the mirror, i.e. virtual. Also $\frac{1}{v} > \frac{1}{f} \Rightarrow v < f$ . Hence $0 < v < f$ : the image lies between the pole and the focus.
½ mark
Solving, $v = \frac{f x}{x + f}$ . Magnification: $m = - \frac{v}{u} = \frac{v}{x} = \frac{f}{x + f}$ .
½ mark
Since $f < x + f$ , we get $0 < m < 1$ . The image is therefore always erect and diminished.
½ mark

Answer: 0 < v < f (between pole and focus, virtual) and 0 < m = f/(x+f) < 1 (diminished, erect).

Where the marks are

Applies the mirror formula with the correct signs for a convex mirror (½ mark)
Shows v is positive and less than f, so the image lies between P and F (½ mark)
Writes m = −v/u in terms of f and x (½ mark)
Concludes m is positive and less than 1, so the image is diminished (½ mark)

Revise the chapter

Chapter: Ray Optics and Optical Instruments (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Ray Optics and Optical Instruments, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 55/7/1: every question, by section.

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CBSE Class 12 Physics 2025: question 18(a)

Hints

Step-by-step solution

Revise the chapter

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