Question

Consider an equiconvex lens of radius of curvature $R$ and focal length $f$. If $f>R$, the refractive index $\mu$ of the material of the lens.

• A. Is greater than zero but less than $1.5$
• B. Is greater than $1.5$ but less than $2.0$
• C. Is greater than $1.0$ but less than $1.5$
• D. None of these

Answer 1

The correct option is C Is greater than $1.0$ but less than $1.5$

$\frac{1}{f}=(\mu -1)\left(\frac{2}{R}\right)$

or $f=\frac{R}{2(\mu -1)}$

Now, $f>R$

$\therefore \frac{R}{2(\mu -1)}>R$

or $\frac{1}{2(\mu -1)}>1$ or $2(\mu -1)<1$

or $\mu -1<\frac{1}{2}$ or $\mu <(1+\frac{1}{2})$ or $\mu <1.5$.