An object is placed in front of a convex mirr | vedclass

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(B) Since there is no parallax,it means that both images (formed by the plane mirror and the convex mirror) coincide with each other.According to the

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$25$

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(B) Since there is no parallax,it means that both images (formed by the plane mirror and the convex mirror) coincide with each other.According to the property of a plane mirror,it will form an image at a distance of $30\, cm$ behind it. The plane mirror is placed at a distance of $30\, cm$ from the object and $20\, cm$ from the convex mirror (since the total distance is $50\, cm$).The image formed by the plane mirror is $30\, cm$ behind the plane mirror. Therefore,the distance of this image from the convex mirror is $20\, cm + 30\, cm = 50\, cm$ behind the convex mirror.For the convex mirror,the object distance is $u = -50\, cm$ and the image distance is $v = +50\, cm$.Using the mirror formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$\frac{1}{f} = \frac{1}{50} + \frac{1}{-50} = 0$. This implies $f = \infty$,which is incorrect based on the provided diagram. Let's re-evaluate based on the diagram: The image is formed at $10\, cm$ behind the convex mirror. Thus,$v = +10\, cm$ and $u = -50\, cm$.$\frac{1}{f} = \frac{1}{10} + \frac{1}{-50} = \frac{5-1}{50} = \frac{4}{50} = \frac{2}{25}$$f = \frac{25}{2}\, cm$$R = 2f = 2 	imes \frac{25}{2} = 25\, cm$.

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