in an experiment a convex lens of focal length15cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5cm from it. It is found that an object and its image coincide ,if the object is placedat a distance of 20cm from the lens. the focal length of the convex mirror is ;

Answers (1)

\begin{aligned} &\text { for convex lens: }\\ &\mathrm{u}=-20 \mathrm{cm}, \quad \mathrm{f}=15 \mathrm{cm}\\ &\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ &\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{f}}+\frac{1}{\mathrm{u}}\\ &\frac{1}{\mathrm{v}}=\frac{1}{15}+\left(\frac{1}{-20}\right) \end{aligned}

\mathrm{v}=\frac{-15 \times 20}{-20+15}=\frac{300}{5}=60 \mathrm{cm}$
for mirror:
$\mathrm{u}=55 \mathrm{cm}, \quad \mathrm{f}=?$ 
for the mirror to form image at '0':
\mathrm{u}=\mathrm{R}=2 \mathrm{f} \\ \\ \mathrm{f}=\frac{\mathrm{R}}{2}=27.5 \mathrm{cm}

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