A slanted object \(A B\) is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:

Location of image of \(\mathrm{A}:-\)
\(\begin{aligned} & \frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \Rightarrow \frac{1}{\mathrm{v}}-\frac{1}{-30}=\frac{1}{20} \Rightarrow \frac{1}{\mathrm{v}}=\frac{1}{60} \Rightarrow \mathrm{v}=60 \mathrm{~cm} \\ & \therefore \mathrm{~m}=2\end{aligned}\)
Since size of object is small wrt the location hence
\(\begin{aligned} & d v=m^2 d u \Rightarrow d v=4 \times 1=4 \mathrm{~cm} \\ & h_i=m h_0 \Rightarrow h_i(d y)=2 \times 2=4 \mathrm{~cm}\end{aligned}\)
\(\therefore\) Angle made with principle axis \(=-45^{\circ}\)