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 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:
Updated On: Apr 10, 2026
- 0.5
- 2.5
- 0.8
- 1.25
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
The focal length of a lens depends on the refractive index of its material and the radii of curvature of its two surfaces. This relationship is described by the Lens Maker's Formula. For a biconvex lens, the first surface has a positive radius of curvature and the second has a negative radius of curvature.
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: \( R_1 = R \) and \( R_2 = -R \).
Step 3: Detailed Explanation:
Given the refractive index \( \mu = 1.4 \).
Using the sign convention for a biconvex lens with equal radii:
\[ \frac{1}{f} = (1.4 - 1) \left( \frac{1}{R} - \left(-\frac{1}{R}\right) \right) \]
\[ \frac{1}{f} = (0.4) \left( \frac{1}{R} + \frac{1}{R} \right) \]
\[ \frac{1}{f} = 0.4 \times \frac{2}{R} \]
\[ \frac{1}{f} = \frac{0.8}{R} \]
Taking the reciprocal to find the focal length \( f \):
\[ f = \frac{R}{0.8} = \frac{R}{4/5} = 1.25R \]
The required ratio of focal length to radius of curvature is:
\[ \frac{f}{R} = 1.25 \]
Step 4: Final Answer:
The ratio of its focal length and radius of curvature is 1.25.
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