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A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?

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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...
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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=v1u1

Where:

  • flensflens is the focal length of the lens,
  • vv is the image distance (which is 20 cm since the image coincides with the object),
  • uu is the object distance (given as 20 cm).

Substituting the given values:

1flens=120−120flens1=201201

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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