# A convex mirror and a concave mirror each of focal length 10cm are placed coaxially. They are separated by 40cm and their reflecting surface face each other. A point object is kept on the principle axis at a distance X cm from the concave mirror such that final image after two reflections, first on the concave mirror, is on the object itself. Find the integer next to X.

Grade:12th pass

## 1 Answers

Yashasvi yadav
28 Points
4 years ago
Firstly we find v for concave mirror
V=uf/u-f => V=(-x)(-10)/-x+10
V =10x/10-x now if this term is positive then image will be formed behind concave mirror and the image formed by convex mirror will never lie on object .so this v is -ve   and v-40 will be u for convex mirror  so u=v-40=[-10x/10-x ]-40 = 30x-400 /10-x .
So for convex  mirror    u=30x-400/10-x ; v =-(40-x)=x-40 ;f=10
Applying mirror formula
V=uf/u-f
x-40=(30x-400 /10-x)(10) /[(30x -400)/10-x]-10
So we get quadratic on solving as
x²-60x+600=0 so X=25.35/2 =12.677
So integer next to x is 13 is the required answer ,regards

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