a. The height of image of pencil will be 116 cm.
b. The image will formed at distance of 140 cm from the lens.
a. The lens equation is given as,
[tex]\frac{1}{f} =\frac{1}{v}+\frac{1}{u}\\
[/tex]
Where u is distance of object from lens, v is distance of image from lens and f is focal length.
Given that, [tex]u=35cm,f=28cm[/tex]
Substitute values in above equation.
[tex]\frac{1}{28}=\frac{1}{v} +\frac{1}{35}\\
\\
\frac{1}{v}=\frac{1}{28}-\frac{1}{35} =\frac{5-4}{140} =\frac{1}{140}\\
\\
v=140cm[/tex]
The image will formed at distance of 140 cm from the lens.
b. Magnification is given as,
[tex]m=\frac{v}{u}=\frac{h_{i}}{h_{o}} [/tex]
Here, [tex]h_{i}[/tex] is height of image and [tex]h_{0}[/tex] is height of object.
[tex]\frac{h_{i}}{29}=\frac{140}{35}=4\\
\\
h_{i}=29*4=116cm[/tex]
The height of image of pencil will be 116 cm.
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