question_answer

The image of a small electric bulb fixed on the wall of a room is to b6 obtained on the opposite wall 4 m away by means of a large convex lens. The maximum possible focal length of the lens required for this purpose will be :

A)  0.5 m           

B)  1.0 m

C)  1.5m          

D)  2.0m

Correct Answer: B

Solution :

Let a large convex lens is placed between two walls at a distance x from wall on which an electric bulb is fixed. Using     \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\]                 \[=\frac{1}{4-x}-\frac{1}{-x}[\therefore \,u=-x,\,v=4-x]\]                 \[\frac{4}{(4-x)\,(x)}\] or            \[f=\frac{(4-x)\,x}{4}\] ... (i) Now, magnification \[m=\frac{v}{u}=\frac{4-x}{x}\] \[\Rightarrow \] \[1=\frac{4-x}{x}\] \[\Rightarrow \] \[x=4-x\] \[\Rightarrow \] \[2x=4\] \[\Rightarrow \] \[x=2\,m\] Hence, from Eq. (i), we get                 \[f=\frac{(4-2)\,(2)}{4}\] \[=\frac{2\times 2}{4}=1\,m\]