KCET · Physics · Ray Optics
The power of a equi-concave lens is \(-4.5 \mathrm{D}\) and is made of a material of refractive index 1.6, the radii of curvature of the lens is
- A \(36.6 \mathrm{~cm}\)
- B \(-266 \mathrm{~cm}\)
- C \(115.44 \mathrm{~cm}\)
- D \(-26.6 \mathrm{~cm}\)
Answer & Solution
Correct Answer
(D) \(-26.6 \mathrm{~cm}\)
Step-by-step Solution
Detailed explanation
Power of equi-concave lens, \(P=-4.5 \mathrm{D}\)
Refractive index, \(\mu=1.6\)
Focal length of lens,
\[
f=\frac{1}{P}=\left(\frac{1}{-4.5}\right) \mathrm{m}=\left(\frac{100}{-4.5}\right) \mathrm{cm}=\left(\frac{-200}{9}\right) \mathrm{cm}
\]
By lens Maker's formula, we get
\[
\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)
\]
For equi-concave lens,
\[
R_1=-R \text { and } R_2=R
\]
Putting these values in Eq. (i), we get
\[
\begin{aligned}
& \frac{1}{200 / 9}=(1.6-1)\left(\frac{1}{-R}-\frac{1}{R}\right) \Rightarrow \frac{9}{200}=0.6\left(\frac{-2}{R}\right) \\
& \Rightarrow \quad R=\frac{-0.6 \times 2 \times 200}{9}=-26.6 \mathrm{~cm}
\end{aligned}
\]
Refractive index, \(\mu=1.6\)
Focal length of lens,
\[
f=\frac{1}{P}=\left(\frac{1}{-4.5}\right) \mathrm{m}=\left(\frac{100}{-4.5}\right) \mathrm{cm}=\left(\frac{-200}{9}\right) \mathrm{cm}
\]
By lens Maker's formula, we get
\[
\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)
\]
For equi-concave lens,
\[
R_1=-R \text { and } R_2=R
\]
Putting these values in Eq. (i), we get
\[
\begin{aligned}
& \frac{1}{200 / 9}=(1.6-1)\left(\frac{1}{-R}-\frac{1}{R}\right) \Rightarrow \frac{9}{200}=0.6\left(\frac{-2}{R}\right) \\
& \Rightarrow \quad R=\frac{-0.6 \times 2 \times 200}{9}=-26.6 \mathrm{~cm}
\end{aligned}
\]
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