Answer:
88.89 cm
Explanation:
We are given that
Distance between bulb and wall=4 m=[tex]4\times 100=400 cm[/tex]
1 m=100 cm
Let h be the height of object
Object distance=-u
Image distance= v
Height of object=2h
Magnification=[tex]\frac{h'}{h}=\frac{v}{u}[/tex]
[tex]\frac{2h}{h}=\frac{v}{u}[/tex]
[tex]v=2u[/tex]
Lens formula
[tex]\frac{1}{f}=\frac{1}{v}-\frac{1}{u}[/tex]
[tex]\frac{1}{f}=\frac{1}{2u}+\frac{1}{u}[/tex]
[tex]\frac{1}{f}=\frac{1+2}{2u}=\frac{3}{2u}[/tex]
[tex]f=\frac{2u}{3}[/tex]
[tex]v+u=400 cm[/tex]
[tex]2u+u=400[/tex]
[tex]3u=400[/tex]
[tex]u=\frac{400}{3} cm[/tex]
[tex]f=\frac{2}{3}\times \frac{400}{3}=\frac{800}{9}[/tex]
[tex]f=88.89 cm[/tex]
