Assertion and Reason for Concave Mirror and Image at Infinity – Rankers Physics

Reflection by Spherical Mirrors: Practice Problem & Solution

Assertion (A): Radius of curvature of a concave mirror is \(20 \text{cm}\). If a real object is placed in front of a mirror at \(10 text{cm}\) from pole of the mirror, image is formed at infinity. Reason (R): When object is placed at focus of a converging optical system then its image is formed at infinity.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Reflection by Spherical Mirrors. Understanding the underlying formula is key to arriving at the correct answer below:

For a concave mirror, \(R = 20 \text{cm}\), so \(f = R/2 = 10 \text{cm}\). An object placed at the focal point of a converging mirror forms its image at infinity. Both A and R are true, and R correctly explains A.

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): A point object is placed at a distance of \(26 \text{ cm}\) from a convex mirror of focal length \(26 \text{ cm}\). The image will form at infinity. Reason (R): For above given system the equation \(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\) gives position of image.  
2. Assertion (A): The formula \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) connecting u and v for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvatures. Reason (R): Laws of reflection are strictly valid for smaller size of optical system.  
3. For a prism its refractive index is $\cot A/2$ then minimum angle of deviation is: (1999)
4. Assertion (A): The focal length of a spherical mirror does not depend on the wavelength of light. Reason (R): In case of reflection of light from a denser medium the phase changes by \(\pi\).  
5. Assertion (A): In total internal reflection reflected light is in the phase with incident light. Reason (R): Reflecting surface is rarer in TIR.