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CBSE Class 12-science Answered

A point object O is kept at a distance of 30 cm of a convex lens power +4D towards its left.It is observed that when a convex mirror is kept on the right side at a distance of 50 cm of the convex lens ,the image of the object O formed by the lens mirror combination with the object itself.Calculate the focal length of the convex mirror.
Asked by Balbir | 25 Feb, 2018, 11:32: AM
answered-by-expert Expert Answer
 
The given problem is illustrated in the above schematic diagram(not to the scale).
power of the given convex lens = +4D ; hence focal length 25 cm.
If the object is at a distance 30 cm from lens on left side, the inverted image will be formed at 150 cm from lens on right side as per the calculation given below
begin mathsize 12px style 1 over v minus 1 over u equals 1 over f space space semicolon space space space 1 over v plus 1 over 30 equals 1 over 25 semicolon space w e space g e t space v space equals space 150 space c m end style
 
since mirror is at 50 cm from the lens on right side, object-to-mirror distance for convex mirror is 100 cm and image-to-mirror distance is 80 cm.
we can get the focal length of the mirror as follows
begin mathsize 12px style 1 over v plus 1 over u space equals 1 over f semicolon space v space equals space minus 80 semicolon space u space equals space 100 semicolon minus 1 over 80 plus 1 over 100 equals 1 over f semicolon space w e space g e t space f space equals negative 400 space c m end style
hence focal length of convex mirror is 400 cm
Answered by Thiyagarajan K | 25 Feb, 2018, 01:40: PM
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