a plane mirror is placed at a distance 12.5 cm from the focus of a concave mirror of radius curvature 20cm find where the object can be placed between the two Mirrors of the first image in the both of the Mirrors concide
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Expert's answer
2020-10-16T11:07:29-0400
Radius of curvature of the mirror is (R)=20cm
Hence, focal length of concave mirror, f=2−R=−10cm
As per the question, plane mirror is placed at a distance of 12.5 cm from the focus of concave mirror.
Let an object is placed x distance from plane mirror.
then, image distance from plane mirror = x cm right side of plane mirror.
so, image distance v=−(12.5+10−x)=−(22.5−x) from concave mirror
again,
object distance from concave mirror, u=−(x+12.5+10)=−(x+22.5)cm
using mirror formula,
v1−u1=f1
⇒(22.5−x)−1−(x+22.5)1=−101
⇒(22.52−x2)−(22.5+x)−(22.5−x))=−101
⇒(22.52−x2)−45=−101
⇒450=22.52−x2
⇒x2=506.25−450
⇒x2=56.25cm2
⇒x=56.25cm
⇒x=7.5cm
hence, object is placed 7.5 cm left side from plane mirror.
Comments
Your answer (12.5 cm) is wrong, the correct answer for this question is 7.5 cm. Hope you try solving it again and change it.
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