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A biconvex lens $\left(\mathrm{R}_1=\mathrm{R}_2=30\right)$ has focal length equal to the focal length of concave mirror. The radius of curvature of concave mirror is
[Refractive index of material of lens $=1.6]$
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[Refractive index of material of lens $=1.6]$
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Verified Answer
The correct answer is:
50 cm
For a biconvex lens
$$
\begin{aligned}
& \frac{1}{\mathrm{f}}=(\mu-1)\left(\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right) \\
& =(1.6-1)\left(\frac{1}{30}+\frac{1}{30}\right) \\
& =0.6 \times \frac{2}{30}=\frac{1.2}{30} \\
& \mathrm{f}=\frac{30}{1.2}=25 \mathrm{~cm}
\end{aligned}
$$
Radius of concave mirror $=2 \mathrm{f}=50 \mathrm{~cm}$
$$
\begin{aligned}
& \frac{1}{\mathrm{f}}=(\mu-1)\left(\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right) \\
& =(1.6-1)\left(\frac{1}{30}+\frac{1}{30}\right) \\
& =0.6 \times \frac{2}{30}=\frac{1.2}{30} \\
& \mathrm{f}=\frac{30}{1.2}=25 \mathrm{~cm}
\end{aligned}
$$
Radius of concave mirror $=2 \mathrm{f}=50 \mathrm{~cm}$
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