Question

A concave mirror forms an image at twice the focal length from the mirror. What is the nature and size of the image compared to the object?

• A. Real, inverted, same size
• B. Real, inverted, magnified
• C. Virtual, erect, magnified
• D. Virtual, erect, diminished

Hint:

In concave mirrors, placing the object at center of curvature produces a real, inverted image of the same size at the center of curvature.

Answer 1

The Correct Option is A

A concave mirror forms an image at twice its focal length, a scenario where we need to analyze the image characteristics using a lens/mirror equation. For a mirror, this equation is:

1/f = 1/v + 1/u

Where:

• f is the focal length of the mirror.
• v is the image distance from the mirror.
• u is the object distance from the mirror.

Given that the image distance v is twice the focal length, i.e., v = 2f. Substituting in the lens/mirror equation:

1/f = 1/(2f) + 1/u

Simplifying, we get:

1/u = 1/f - 1/(2f) = (2-1)/(2f) = 1/(2f)

Thus, u = 2f. This indicates that the object is also placed at twice the focal length. In this case, the object is at the center of curvature.

For a concave mirror, when the object is placed at the center of curvature, several characteristics of the image are observed:

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

Thus, the correct answer is: Real, inverted, same size.