Question

an object is placed at a distance of 2f from a concave mirror of focal length f the image distance is
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Answer 1

For a concave mirror, when object is at 2f. image is formed at 2f.

For a concave mirror, when object is at 2f. image is formed at 2f.Hence, v1=−2f for concave mirror

For a concave mirror, when object is at 2f. image is formed at 2f.Hence, v1=−2f for concave mirrorImage formed by concave mirror serves as an object to plane mirror.

For a concave mirror, when object is at 2f. image is formed at 2f.Hence, v1=−2f for concave mirrorImage formed by concave mirror serves as an object to plane mirror.Position of plane mirror with respect to concave mirror is d=−f

For a concave mirror, when object is at 2f. image is formed at 2f.Hence, v1=−2f for concave mirrorImage formed by concave mirror serves as an object to plane mirror.Position of plane mirror with respect to concave mirror is d=−f 

For a concave mirror, when object is at 2f. image is formed at 2f.Hence, v1=−2f for concave mirrorImage formed by concave mirror serves as an object to plane mirror.Position of plane mirror with respect to concave mirror is d=−f Hence, position of object for plane mirror is, u2=−f, (origin shifted to left)

For a concave mirror, when object is at 2f. image is formed at 2f.Hence, v1=−2f for concave mirrorImage formed by concave mirror serves as an object to plane mirror.Position of plane mirror with respect to concave mirror is d=−f Hence, position of object for plane mirror is, u2=−f, (origin shifted to left)Hence, position of image for plane mirror is, v2=+f

For a concave mirror, when object is at 2f. image is formed at 2f.Hence, v1=−2f for concave mirrorImage formed by concave mirror serves as an object to plane mirror.Position of plane mirror with respect to concave mirror is d=−f Hence, position of object for plane mirror is, u2=−f, (origin shifted to left)Hence, position of image for plane mirror is, v2=+fPosition of final image wrt the concave mirror is v3=v2+d=0, (origin shifted to right)

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Answer 2

Given : For concave mirror ,object is placed at a distance of 2f .

To Find : Image distance

Solution :

For a concave mirror, when object is at 2f ( u = -2f) and focal length is negative.

From mirror formulae,

$\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\]$    

$\[\frac{1}{v} = - \frac{1}{f} + \frac{1}{{2f}}\]$                                                         (as u = -2f)      

v = -2f

Hence, when object is placed at a distance of 2f from a concave mirror the image distance is 2f.