A convex lens is made from glass material having refractive index of $1.4$ with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is $____$.

Question

Accepted Answer

C. 1. For a thin lens, the **Lens Maker's formula** is

$$
\frac{1}{f}
=
(n-1)
\left(
\frac{1}{R_1}
-
\frac{1}{R_2}
\right),
$$

where:

* $f$ is the focal length,
* $n$ is the refractive index of the lens material,
* $R_1$ and $R_2$ are the radii of curvature of the two surfaces.

2. The lens is **equi-convex**, so both surfaces have the same radius of curvature $R$.

According to the Cartesian sign convention,

$$
R_1=+R,\qquad
R_2=-R.
$$

3. Substituting these values,

$$
\frac{1}{f}
=
(1.4-1)
\left(
\frac{1}{R}
-
\frac{1}{-R}
\right).
$$

Simplifying,

$$
\frac{1}{f}
=
0.4
\left(
\frac{2}{R}
\right)
=
\frac{0.8}{R}.
$$

4. Therefore,

$$
f=\frac{R}{0.8}.
$$

Hence,

$$
\frac{f}{R}
=
\frac{1}{0.8}
=
1.25.
$$

5. Therefore, the required ratio is **1.25**, so the correct option is **C**.

A convex lens is made from glass material having refractive index of 1.41.41.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ____.

A convex lens is made from glass material having refractive index of $1.4$ with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is $____$ .