An object is placed 60 cm in front of a conv | vedclass

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Question

(A) For the convex mirror, the object distance $u = -60 \ cm$ and focal length $f = +30 \ cm$.Using the mirror formula $\frac{1}{v} + \frac{1}{u} = \f

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) For the convex mirror, the object distance $u = -60 \ cm$ and focal length $f = +30 \ cm$.Using the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$:$\frac{1}{v} + \frac{1}{-60} = \frac{1}{30}$$\frac{1}{v} = \frac{1}{30} + \frac{1}{60} = \frac{2+1}{60} = \frac{3}{60} = \frac{1}{20}$So, $v = +20 \ cm$ (behind the mirror).The image formed by the convex mirror is at a distance of $20 \ cm$ behind the mirror.The total distance of this image from the object is $60 \ cm + 20 \ cm = 80 \ cm$.Let the plane mirror be placed at a distance $x$ from the object. The image formed by the plane mirror will be at a distance $x$ behind the plane mirror.For no parallax, the image formed by the plane mirror must coincide with the image formed by the convex mirror.The distance of the plane mirror's image from the object is $2x$.Equating the distances: $2x = 80 \ cm$, which gives $x = 40 \ cm$.

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