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