A Square Wire Of Side 3.0 Cm Is Placed 25 Cm Away From A Concave Mirror Of Focal Length 10 Cm. What Is The Area Enclosed By The Image Of The Wire? The Centre Of The Wire Is On The Axis Of The Mirror, With Its Two Sides Normal To The Axis.  

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Question

A square wire of side 3.0 cm is placed 25 cm away from a concave mirror of focal length 10 cm. What is the area enclosed by the image of the wire? The centre of the wire is on the axis of the mirror, with its two sides normal to the axis.  

Solution

Correct option is

4.0 cm2

 

In usual notations, we have

                                    

The distance v of image from the mirror is given by

                                  

   

The negative sign indicates that the image is formed on the same side as the object, that is, infront the mirror.  

The magnification is  

                                   

Since the magnification is negative, the image is real (inverted).

Now, the side of the square is 3.0 cm, that is, y1 = +3.0 cm. The side of the image of the square is given by (m = y2/y1)   

                                

∴ area enclosed by the image of the square is

                                                     (–2.0 cm) × (–2.0 cm) = 4.0 cm2

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