A concave mirror is fixed on the ground with its principle axis vertical and its reflecting surface facing upwards, and filled with water (refractive index 
). A small object is placed on the axis of the mirror at a distance 120 cm from it. The final image of the object is coincident with it. The focal length (in cm ) of the mirror is .
Text Solution
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(80) The water "lens" and the mirror behave together like a concave mirror
If the focal length of the original concave mirror is 
, its radius of curvature is 
Now, the focal length of the water "lens" is given by
So, the equivalent focal length of the combination of the water "lens" and the original concave mirror is given by
For the image to be coincident with the object, the object should be at the centre of curvature of the combination mirror
So, 
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