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?
Show Hint
- Real, inverted, same size
- Real, inverted, magnified
- Virtual, erect, magnified
- Virtual, erect, diminished
The Correct Option is A
Solution and Explanation
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.
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