Question

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:

• A. 0.5
• B. 2.5
• C. 0.8
• D. 1.25

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The focal length of a thin lens is determined by the refractive index of its material and the radii of curvature of its two surfaces. For a biconvex lens with symmetric surfaces, we can use the Lens Maker's Formula to find a direct relation between the focal length $f$ and the radius $R$.
Step 2: Key Formula or Approach:
Lens Maker's Formula:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] For an equiconvex lens, by sign convention: $R_1 = +R$ and $R_2 = -R$.
Step 3: Detailed Explanation:
Given the refractive index $\mu = 1.4$.
Substitute the radii into the Lens Maker's Formula:
\[ \frac{1}{f} = (1.4 - 1) \left( \frac{1}{R} - \left( -\frac{1}{R} \right) \right) \] \[ \frac{1}{f} = (0.4) \left( \frac{1}{R} + \frac{1}{R} \right) \] \[ \frac{1}{f} = 0.4 \times \frac{2}{R} \] \[ \frac{1}{f} = \frac{0.8}{R} \] We need the ratio of focal length to radius of curvature, which is $\frac{f}{R}$.
Rearranging the equation:
\[ \frac{f}{R} = \frac{1}{0.8} = \frac{10}{8} = 1.25 \] Step 4: Final Answer:
The ratio is 1.25.