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Question
An object kept on the principal axis and infront of a spherical mirror, is moved along the axis itself. Its lateral magnification m is measured, and plotted versus object distance |u| for a range of u, as shown in fig. The magnification of the object when it is placed at a distance 20 cm in front of the mirror is:
An object kept on the principal axis and infront of a spherical mirror, is moved along the axis itself. Its lateral magnification m is measured, and plotted versus object distance |u| for a range of u, as shown in fig. The magnification of the object when it is placed at a distance 20 cm in front of the mirror is:
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Solution
The correct option is A −1
We need to find the focal length f of the mirror. From graph we can notice that when object distance u is -5 cm then the lateral magnification is 2.
As magnification = −Image distanceObject distance.
So the image distance: v=−2×5=−10 cm.
From the mirror equation, f=−10 cm.
Now when u is −20 cm, using the mirror equation,
v=−20 cm, or the image is at the center of curvature of the spherical mirror.
So the magnification here is =−(−20)(−20)=−1
We need to find the focal length f of the mirror. From graph we can notice that when object distance u is -5 cm then the lateral magnification is 2.
As magnification = −Image distanceObject distance.
So the image distance: v=−2×5=−10 cm.
From the mirror equation, f=−10 cm.
Now when u is −20 cm, using the mirror equation,
v=−20 cm, or the image is at the center of curvature of the spherical mirror.
So the magnification here is =−(−20)(−20)=−1
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