A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the objec ? Also, find the power of the lens.

A convex lens forms a real and inverted image of a needle at a distanc

1.	A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the objec ? Also, find the power of the lens.
Answer» Solution :As REAL and INVERTED IMAGE of a needle is formed by convex LENS at a distance of 50 cm from it, hence `upsilon = +50` cm. As size of image = size of object, hence h. = h. But `(h.)/(h) = (upsilon)/(u)` `rArr""u = (upsilon h)/(h.) = (50 XX h)/(h) = 50` cm So, the needle is placed 50 cm in front of convex lens as per sign convention u = -50 cm. Now `(1)(v) - (1)/(u) = (1)/(f)` `therefore""(1)/(f) = (1)/((50)) - (1)/((-50)) = (1)/(50) + (1)/(50) = (1)/(25)` cm `rArr""f` = +25 cm = +0.25 m `therefore` Power of the lens `P = (1)/(f(m)) = (1)/(0.25 m) = +4D`