Question

A 2.0 cm tall object is perpendicular to principal axis of a convex lens of focal length 10 cm . Distance of object from lens is 15cm. Find nature,,position and size of image and also find magnification

Answer 1

Dear Student
$$\begin{gathered} HeightofobjectO=+2cm \\ f=+10cm \\ u=-15cm \\ \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ \frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{10}+\frac{1}{(-15)} \\ \frac{1}{v}=\frac{3-2}{30} \\ v=30cm \\ Positivesignindicatesthatimageformedbehindthelens \\ Thereforeimageisreal \\ m=\frac{v}{u}=\frac{I}{O} \\ \frac{30}{-15}=\frac{I}{2} \\ Heightofimage=-4cm \\ Negativesignindicatesthatimageisinverted. \\ m=\frac{I}{O}=\frac{-4}{2}=-2 \\ Imageis2timesenlarged. \end{gathered}$$
Regards