When an object is kept at a distance $ 20 ext{ cm}$ in front of a concave mirror, a real image is formed at t

Question

When an object is kept at a distance $ 20	ext{ cm}$ in front of a concave mirror, a real image is formed at the centre of curvature of the mirror. Magnification produced by the mirror is ________.

Examoogle · Accepted Answer

The correct answer is Option B: 1. When an object is placed at the centre of curvature ($C$) of a concave mirror (at distance $u = -20$ cm), its real and inverted image is also formed at the centre of curvature ($v = -20$ cm). The magnification $m$ for this mirror is given by $m = -\frac{v}{u} = -1$, indicating that the image is real, inverted, and of the same size as the object.

Step-by-Step Solution & Concepts:
When an object is placed at the centre of curvature ($C$) of a concave mirror (at distance $u = -20$ cm), its real and inverted image is also formed at the centre of curvature ($v = -20$ cm). The magnification $m$ for this mirror is given by $m = -\frac{v}{u} = -1$, indicating that the image is real, inverted, and of the same size as the object.

Working Principle: For a concave mirror, when the object distance $u$ is equal to twice the focal length ($u = -2f = -R$), the image distance $v$ is also equal to $-2f$. Using the mirror formula $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$, we get equal image and object distances. The magnification $m = -\frac{v}{u}$ evaluates to $-1$ because both $v$ and $u$ are negative and equal in magnitude.

Key Formulas: $m = -\frac{v}{u}$ — Linear magnification for spherical mirrors; $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ — Mirror formula; $R = 2f$ — Radius of curvature and focal length relation

Key Points: When an object is placed at $C$ of a concave mirror, the real and inverted image is also formed at $C$.; Object distance $u = -20$ cm, Image distance $v = -20$ cm.; Magnification $m = -1$ indicates that the image size is equal to the object size and the image is inverted.; The negative sign of magnification represents that the image is real and inverted.

Advantages: Helps in accurately determining the focal length and radius of curvature of mirrors.; Provides a direct method to verify magnification formulas.

Disadvantages: Only applicable under paraxial ray approximations for spherical mirrors.

Applications: Optical bench experiments in physics laboratories; Reflecting telescopes and optical focusing setups

Additional Info: Option A (-20): Incorrect; this is the object/image distance value, not magnification.. Option B (-1): Correct; calculated using $m = -v/u$.. Option C (-10): Incorrect arithmetic or confusion with focal length.. Option D (-0.5): Incorrect magnification value.

Answer: B is correct — Magnification produced by the concave mirror is -1 because the image is formed at the same distance as the object at the centre of curvature with equal size and inverted orientation.

Exam Tip: Always remember sign conventions: distances measured against the direction of incident light are taken as negative in Cartesian sign conventions for mirrors.

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