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CBSE Class 12-science Answered

establish the relation 1/u+1/v=1/f for a concave mirror forming virtual image
Asked by uttam kumar | 23 Feb, 2015, 09:31: AM
answered-by-expert Expert Answer

 

In the figure shown above, an object AB is placed in front of a concave mirror between the pole and principal focusof the mirror. Hence, the image formed is virtual, erect and magnified.

Form the figure we get:

begin mathsize 14px style fraction numerator CB over denominator CB apostrophe space end fraction space equals space fraction numerator PB over denominator PB apostrophe end fraction space minus negative negative negative negative left parenthesis Eqn. space 1 right parenthesis Also comma space CB space equals space PC space minus space PB space and space CB apostrophe space equals space PC space plus space PB apostrophe Therefore comma space fraction numerator CB over denominator CB apostrophe space end fraction space equals space fraction numerator space PC space minus space PB over denominator PC space plus space PB apostrophe end fraction space equals space fraction numerator PB over denominator PB apostrophe end fraction space left parenthesis From space eqn. space left parenthesis 1 right parenthesis right parenthesis straight A divided by straight C space to space Cartesian space sign space convention comma Object space distance space left parenthesis PB right parenthesis space equals space minus straight u space Image space distance space left parenthesis PB ’ right parenthesis space equals space plus straight v space Radius space of space curvature space left parenthesis PC right parenthesis space equals space minus straight R fraction numerator negative straight R space plus space straight u over denominator negative straight R space plus space straight v end fraction space equals space fraction numerator negative space straight u over denominator straight v end fraction OR comma space uR space minus space uv space equals space minus vR space plus space uv OR thin space uR space plus space vR space equals space 2 uv Dividing space both space the space sides space by space uvR comma space we space get space 1 over straight v space plus space 1 over straight u space equals space 2 over straight R OR space 1 over straight v space plus space 1 over straight u space equals space 1 over straight f end style


Answered by Yashvanti Jain | 11 Dec, 2017, 07:01: PM

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