Answer to Question #89288 in Optics for Pritish Majumdar

Question #89288
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(R)=20cm

Hence, focal length of concave mirror, f=R2=10cmf =\frac{-R}{2}= -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+10x)=(22.5x)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)cmu = -(x + 12.5 + 10) = -(x+ 22.5)cm

using mirror formula,

1v1u=1f\frac{1}{v} -\frac{ 1}{u} = \frac{1}{f}


1(22.5x)1(x+22.5)=110\Rightarrow \frac{-1}{(22.5-x)} -\frac{ 1}{(x+22.5)} = \frac{1}{-10}


(22.5+x)(22.5x))(22.52x2)=110\Rightarrow \frac{-(22.5+x)-(22.5-x))}{(22.5^2-x^2)} = \frac{1}{-10}


45(22.52x2)=110\Rightarrow \frac{-45}{(22.5^2-x^2)} = \frac{1}{-10}


450=22.52x2\Rightarrow 450=22.5^2-x^2

x2=506.25450\Rightarrow x^2=506.25-450

x2=56.25cm2\Rightarrow x^2=56.25cm^2

x=56.25cm\Rightarrow x=\sqrt{56.25}cm

x=7.5cm\Rightarrow x=7.5cm

hence, object is placed 7.5 cm left side from plane mirror.


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Comments

Anubhav Mishra
15.10.20, 09:18

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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