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Physics-

General

Easy

Question

In the shown figure $M subscript 1 end subscript$ and $M subscript 2 end subscript$ are two concave mirrors of the same focal length 10 cm. AB and CD are their principal axes respectively. A point object O is kept on the line AB at a distance 15 cm from $M subscript 1 end subscript$ . The distance between the mirrors is 20 cm. Considering two successive reflections first on M1 and then on $M subscript 2 end subscript$ . The distance of final image from the line AB is

3 cm
1.5 cm
4.5 cm
1 cm

The correct answer is: 1.5 cm

For M₁
$table row cell v equals fraction numerator u f over denominator u minus f end fraction equals fraction numerator negative 15 cross times open parentheses negative 10 close parentheses over denominator negative 15 minus open parentheses negative 10 close parentheses end fraction equals negative 30 c m end cell row cell text end text text F end text text o end text text r end text text end text M subscript 2 end subscript u equals 10 c m end cell row cell therefore v equals fraction numerator 10 cross times open parentheses negative 10 close parentheses over denominator 10 minus open parentheses negative 10 close parentheses end fraction equals negative 5 c m end cell end table$
$table row cell text end text text m end text text a end text text g end text text n end text text i end text text f end text text i end text text c end text text a end text text t end text text i end text text o end text text n end text text end text m equals fraction numerator negative v over denominator u end fraction equals negative open parentheses fraction numerator negative 5 over denominator 10 end fraction close parentheses equals fraction numerator 1 over denominator 2 end fraction end cell row cell text end text text s end text text o end text text , end text text end text text d end text text i end text text s end text text t end text text a end text text n end text text c end text text e end text text end text text o end text text f end text text end text text i end text text m end text text a end text text g end text text e end text text end text text f end text text r end text text o end text text m end text text end text C D equals fraction numerator 1 over denominator 2 end fraction cross times 3 equals fraction numerator 3 over denominator 2 end fraction c m end cell row cell therefore text end text text d end text text i end text text s end text text t end text text a end text text n end text text c end text text e end text text end text text o end text text f end text text end text text i end text text m end text text a end text text g end text text e end text text end text text f end text text r end text text o end text text m end text text end text A B equals 3 minus fraction numerator 3 over denominator 2 end fraction equals fraction numerator 3 over denominator 2 end fraction c m end cell end table$

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