question_answer

The image of a small electric bulb fixed on the wall of a room is to be obtained on the oppose 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)         1.5 m                                   

D)         2.0 m

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     \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\]                 \[=\frac{1}{4-x}-\frac{1}{-x}\]     \[[\because \,u=-x,v=4-x]\]                 \[=\frac{4}{(4-x)(x)}\] 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                                 \[f=\frac{(4-2)(2)}{4}\]                 \[=\frac{2\times 2}{4}=1\,m\]