A double convex lens has focal length 25 ~cm . The radius of...

A double convex lens has focal length

25 \mathrm{~cm}

. The radius of curvature of one of the surfaces is doubled of the other. Find the radii, if the refractive index of the material of the lens is 1.5. A double convex lens has focal length 25 ~cm . The radius of curvature of one of the surfaces is doubled of the other.

A double convex lens has focal length 25 ~cm . The radius of curvature of one of the surfaces is doubled of the other.

Options

A $100 \mathrm{~cm}, 50 \mathrm{~cm}$
B $25 \mathrm{~cm}, 50 \mathrm{~cm}$
C $18.75 \mathrm{~cm}, 37.5 \mathrm{~cm}$
D $50 \mathrm{~cm}, 100 \mathrm{~cm}$

Correct answer

C. $18.75 \mathrm{~cm}, 37.5 \mathrm{~cm}$

Step-by-step solution

\begin{aligned} & \frac{1}{\mathrm{f}}=(\mu-1)\left[\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right] \\ & \frac{1}{25}=0.5\left[\frac{1}{\mathrm{R}}-\left(\frac{1}{2 R}\right)\right] \\ & \frac{1}{25}=\frac{0.5}{10}\left[\frac{3}{\mathrm{R}}\right] \\ & \mathrm{R}=\frac{75}{4}=18.75 \\ & \mathrm{R}_1=18.75 \mathrm{~cm}, \mathrm{R}_2=37.5 \mathrm{~cm}\end{aligned}

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