Question

A Plane Mirror Is Placed At A Distance Of 50Cm From A Concave Mirror Of Focal Length 16Cm. If A Short Object Be Placed Between The Mirrors And Facing Both The Mirrors To Each Other So That Its Virtual Image In The Plane Mirror Coincides With The Real Image In Concave Mirror. What Is The Ratio Of The Magnitude Of The Sizes Of The Image Formed By The Plane Mirror To The Size Of The Image Formed By The Concave Mirror?

Answer 1

Answer:

1.12

Explanation:

f=-16

u=-50/2=-25

1/v+1/u=1/f

1/v+1/(-25)=1/-16

1/v=-1/16+1/25

1/v=-9/400

v=-400/9

m=400/9×-50

magnification of plane mirror =1

1/400/9×-50

9×-50/400

=9:8

Answer 2

Answer:

The Ratio Of Sizes Of The Two Images 1:4

Explanation:

TO FIND : The Ratio Of Sizes Of The Two Images .

GIVEN:

      Distance Of Plane mirror  From A Concave Mirror = $50CM$

      Focal Length  Of A Concave Mirror   = $16CM$

A Short Object Be Placed Between The Mirrors And Facing Both The Mirrors To Each Other.

    Virtual Image In The Plane Mirror Coincides With The Real Image In Concave Mirror.

Let us consider the object  is AB and plane mirror of distance  X cm.

Distance between concave mirror and object AB is  = (50-X) CM

  AM = X CM

Let X be the image distance that is formed from plane mirror towards its right of the concave mirror of (50+X) CM

There fore OA= AM + OM

                   OA = (50+X) CM

           The distance of the object from concave mirror  $u= -(50-X)$ CM

            The distance of the image from concave mirror  $v=-(50+X)$ CM

                    Focal length of the concave mirror is $=-16 CM$

    Mirror formula:   $\frac{1}{f} =\frac{1}{u} +\frac{1}{v}$

                        $\frac{-1}{16}= \frac{1}{-(50+X)}+ \frac{1}{-(50-X)}$

                         $\frac{1}{16} =\frac{50-X+50+X}{50^{2}- X^{2} }$

                          $100*16=2500-X^{2}$

                           $X=30CM$

Let the object  is AB and plane mirror of distance  30 cm

 

The Ratio Of the two images is    $\frac{u}{v} =\frac{50-X}{50+X}$

                                                        $\frac{u}{v} =\frac{20}{80} \\\frac{u}{v} =\frac{1}{4}$

The Ratio Of The Magnitude Of The Sizes Of The Image Formed By The Plane Mirror To The Size Of The Image Formed By The Concave Mirror is 1:4

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