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 \[f=\frac{(4-2)\,(2)}{4}\] \[=\frac{2\times 2}{4}=1\,m\]You need to login to perform this action.
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