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Asked by Awdhesh Last Modified
Answer When a convex lens is placed in contact with a plane mirror and an object at a distance of 20 cm on the axis of this combination has its image coinciding with itself, it means that the combination of the convex lens and the plane mirror acts as a "catadioptric" system, where the lens forms a real image and the mirror forms a virtual image. These images coincide, resulting in no net displacement of the object's image.
In this case, the effective focal length (fefffeff) of the combination is equal to the distance between the object and its real image formed by the lens. Since the object's image coincides with itself, the distance between them is 0.
Given that the object is placed at a distance of 20 cm from the combination, the distance between the object and its image formed by the lens is also 20 cm.
Therefore, the effective focal length (fefffeff) of the combination is 20 cm.
However, the focal length of the convex lens (flensflens) can be determined using the lens formula:
1flens=1v−1uflens1=v1−u1
Where:
Substituting the given values:
1flens=120−120flens1=201−201
1flens=0flens1=0
flens=∞flens=∞
The focal length of the convex lens is infinity. This result is consistent with the fact that the combination of the convex lens and the plane mirror forms an image coinciding with the object, indicating that the system acts as a mirror.
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