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A plane mirror ' M ' and a concave mirror ' X ' are kept at a separation of 40 an with their reflecting faces facing each other as shown in figure. An object AB is kept perpendicular to the principal axis in position (1). Considering successive reflections first at mirror ' X ' and then at ' M', a real image is formed in front of 'M at a normal distance 8 am form it. If the object is moved to new position (2), the real image is formed at 20 cm from ' M ' with the reflections as described earlier.
Keeping the object in position (1), if the plane mirror is replaced with a convex mirror ' Y ' of focal length 20 m facing the mirror ' X ' after successive reflections first at ' X ' and then at ' Y ', the final image will be

  1. at distance of fraction numerator 80 over denominator 3 end fraction text end text c m from the pole of mirror X and in front of its reflecting surface.    
  2. at a distance of fraction numerator 40 over denominator 3 end fraction text end text c m from the pole of mirror X and in front of its reflecting surface.    
  3. mid point between X and Y    
  4. at the position (1)    

The correct answer is: at distance of fraction numerator 80 over denominator 3 end fraction text end text c m from the pole of mirror X and in front of its reflecting surface.

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