Question:
A double convex lens is made of a certain material. The refractive index of the material of the lens is \(1.55\) for violet rays and \(1.50\) for red rays. If the focal length of the lens is \(20\) cm for violet rays, then the focal length of the lens for red rays is
A double convex lens is made of a certain material. The refractive index of the material of the lens is \(1.55\) for violet rays and \(1.50\) for red rays. If the focal length of the lens is \(20\) cm for violet rays, then the focal length of the lens for red rays is
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For the same lens:
\[
f\propto \frac{1}{\mu-1}
\]
Higher refractive index implies smaller focal length.
Updated On: Jun 16, 2026
- \(12\) cm
- \(18\) cm
- \(22\) cm
- \(24\) cm
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The Correct Option is C
Solution and Explanation
Concept:
For a lens of fixed shape,
\[
\frac{1}{f}
=
(\mu-1)
\left(
\frac{1}{R_1}-\frac{1}{R_2}
\right)
\]
Hence,
\[
f\propto \frac{1}{\mu-1}
\]
for the same lens.
Step 1: Write the proportional relation. \[ \frac{f_r}{f_v} = \frac{\mu_v-1}{\mu_r-1} \] Given \[ \mu_v=1.55, \qquad \mu_r=1.50, \qquad f_v=20\text{ cm} \]
Step 2: Substitute the values. \[ f_r = 20 \left( \frac{1.55-1}{1.50-1} \right) \] \[ = 20 \left( \frac{0.55}{0.50} \right) \] \[ = 20\times1.1 \] \[ =22\text{ cm} \] \[\begin{aligned} \boxed{22\text{ cm}} \end{aligned}\] Hence, option \(\mathbf{(C)}\) is correct.
Step 1: Write the proportional relation. \[ \frac{f_r}{f_v} = \frac{\mu_v-1}{\mu_r-1} \] Given \[ \mu_v=1.55, \qquad \mu_r=1.50, \qquad f_v=20\text{ cm} \]
Step 2: Substitute the values. \[ f_r = 20 \left( \frac{1.55-1}{1.50-1} \right) \] \[ = 20 \left( \frac{0.55}{0.50} \right) \] \[ = 20\times1.1 \] \[ =22\text{ cm} \] \[\begin{aligned} \boxed{22\text{ cm}} \end{aligned}\] Hence, option \(\mathbf{(C)}\) is correct.
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