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Question

A U shaped wire is placed before a concave mirror having radius of curvature 20cm as shown in figure. Find the total length of the image.
1031502_f7416a8afead48e2b2d7c5e518bdd986.png

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Solution

Given: Radius of curvature, R=20cm
So, focal length, f=R/2=10cm
For part AB,PB=30+10=40cm

So, u=40cm1v=1f1u=110(140)=340
v=403=13.3cm.
So, PB=13.3cm

m=ABAB=(vu)=(13.340)=13.
AB=10/3=3.33cm

For part CD,PC=30, So u=30cm
1v=1f1u=110(130)=115v=15cm=PC

So, m=CDCD=vu=(1530)=12.
CD=5cm

BC=PCPB=1513.3=17cm
So, total length AB+BC+CD=3.3+1.7+5=10cm.

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