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Question

An object is placed at a distance of 15cm from a convex lens of focal length 10cm. On the other side of the lens, a convex mirror is placed at its focus such that the image formed by the combination coincides with the object itself. The focal length of the convex mirror is :

159372_88213794a1104297a1bb0e41427c6a73.PNG

A
20 cm
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B
10 cm
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C
15 cm
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D
30 cm
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Solution

The correct option is B 10 cm
For the lens ,

u=15 ;f=+10

1v1u=1f

1v115=110

v=+30

Distance between mirror and lens is 10 cm then the image is formed at 20cm from the mirror , this becomes object distance for the mirror and the image formed by the mirror serves as the object for lens.

Final image formed by lens is same at the initial position as that of the object
for lens,

v=+15 ; f=+10

1v1u=1f

1151u=110

u=30 , this is the image for the mirror

now for mirror , u=+20 ;v=+20

1v+1u=1f

120+120=1f

f=10 cm, hence option B is correct

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