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CBSE Class 12 Physics 2020 Outside Delhi Set 3 Paper

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Question : 12
Total: 13
A concave mirror forms a real image of an object kept at a distance 9‌cm from it. If the object is taken away from the mirror by 6‌cm, the image size reduces to ‌
1
4
 th of its previous size. Find the focal length of the mirror.
Solution:  
For the 1‌st ‌ position :
‌ Object distance ‌‌=u1=−9‌cm
‌ Image size ‌‌=h1′
‌ Object size ‌‌=h1
Using mirror formula
‌
1
u
+‌
1
v
=‌
1
f
‌ Or, ‌−‌
1
9
+‌
1
v1
=‌
1
f
 .........(i)
‌ Magnification ‌=‌
h1′
h1
=‌
v1
u1
For the 2‌nd ‌ position :
‌ Object distance ‌‌=u2=−15‌cm
‌ Image size ‌‌=h2′=‌
1
4
h1′
‌ Object size ‌‌=h1
Using mirror formula
‌
1
u
+‌
1
v
=‌
1
f
‌‌ Or, ‌‌‌−‌
1
15
+‌
1
v2
=‌
1
f
 ........(ii)
‌‌ Magnification ‌=‌
h2′
h1
=‌
‌
1
4
h1′
h1
=‌
v2
u2
‌‌ Or, ‌‌‌‌
1
4
‌
v1
u1
=‌
v2
u2
‌‌ Or, ‌‌‌v2=‌
5
12
v1
‌‌ Comparing equations (i) and (ii), ‌
‌−‌
1
9
+‌
1
v1
=−‌
1
15
+‌
1
v2
‌‌ Or, ‌‌‌‌
1
15
−‌
1
9
=‌
1
v2
−‌
1
v1
‌‌ Or, ‌‌‌−‌
2
45
=‌
12
5v1
−‌
1
v1
‌‌ Or, ‌‌‌−‌
2
45
=‌
7
5v1
‌∴v1=−‌
63
2
‌cm
Putting in eqn (i),
‌‌‌−‌
1
9
−‌
2
63
=‌
1
f

‌‌ Or, ‌‌‌−‌
1
7
=‌
1
f

‌∴f=‌ focal length ‌=−7‌cm
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