Question

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3m away by a means of large convex lens. What is the maximum possible focal length of the length required for the purpose?
Also prove that maximum distance between an object and its image in case of a convex lens is 4 times the focal length.

Answer 1

Dear Student

$$\begin{gathered} Dis\tan cebetweentheobjectandimaged=3m \\ maximumfocallength{f}_{max}=? \\ Fortherealimagethemaximumfocallengthisgivenby \\ {f}_{max}=\frac{d}{4} \\ {f}_{max}=\frac{3}{4}=0.75m \\ hencethemaximumfocallengthis \\ {f}_{max}=0.75m \end{gathered}$$

$$\begin{gathered} provethatmaximumdis\tan cebetweenanobjectanditsimageincaseofaconvexlensis4timesthefocallength. \\ let{f}_{max}=\frac{d}{4} \\ d=f_{max}\times 4 \\ d=0.74\times 4=3.00m \end{gathered}$$
Regards