Question

The focal length of a concave mirror is 20 cm. The distance at which an object should be placed to get a real image of same size is:

• A. 10 cm
• B. 20 cm
• C. 40 cm
• D. 30 cm Correct Answer: (C) 40 cm Solution:

Hint:

For a concave mirror: \[ \text{Same-size real image} \Rightarrow \text{Object at } C = 2f \] This is one of the most important standard ray-diagram results.

Answer 1

The Correct Option is C

Concept: A concave mirror forms a real image of the same size as the object when the object is placed at the center of curvature. The center of curvature is located at a distance equal to twice the focal length from the pole of the mirror. \[ C = 2f \] At this position:

• The image formed is real.

• The image is inverted.

• The image is of the same size as the object.

• The image is formed at the center of curvature itself.

Step 1: Identify the given focal length. The focal length is \[ f = 20 \text{ cm} \]

Step 2: Calculate the center of curvature. Since \[ C = 2f \] we get \[ C = 2 \times 20 \] \[ C = 40 \text{ cm} \]

Step 3: Determine the required object position. To obtain a real image of the same size as the object, the object must be placed at the center of curvature. Therefore, \[ \boxed{\text{Object distance} = 40\ \text{cm}} \] Hence, the correct option is \(\boxed{(C)}\).