Question:
As shown in the figure, for a biconvex lens the focal length is \( f \) and both radii of curvature are \( R \). Find the value of \( f/R \) (\( \mu = 1.4 \)):
As shown in the figure, for a biconvex lens the focal length is \( f \) and both radii of curvature are \( R \). Find the value of \( f/R \) (\( \mu = 1.4 \)):
Updated On: Apr 9, 2026
- 1.25
- 1.5
- 2
- 2.5
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The focal length of a lens is determined by the Lens Maker's Formula, which relates the focal length to the refractive index of the material and the radii of curvature of its two surfaces.
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 a biconvex lens, using sign convention: \( R_1 = +R \) and \( R_2 = -R \).
Step 3: Detailed Explanation:
Substitute the given values into the formula: \[ \frac{1}{f} = (1.4 - 1) \left( \frac{1}{R} - \frac{1}{-R} \right) \] \[ \frac{1}{f} = 0.4 \left( \frac{1}{R} + \frac{1}{R} \right) \] \[ \frac{1}{f} = 0.4 \left( \frac{2}{R} \right) = \frac{0.8}{R} \] Inverting the equation to find \( f \): \[ f = \frac{R}{0.8} \] To find the ratio \( f/R \): \[ \frac{f}{R} = \frac{1}{0.8} = \frac{10}{8} = 1.25 \]
Step 4: Final Answer:
The value of \( f/R \) is 1.25.
The focal length of a lens is determined by the Lens Maker's Formula, which relates the focal length to the refractive index of the material and the radii of curvature of its two surfaces.
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 a biconvex lens, using sign convention: \( R_1 = +R \) and \( R_2 = -R \).
Step 3: Detailed Explanation:
Substitute the given values into the formula: \[ \frac{1}{f} = (1.4 - 1) \left( \frac{1}{R} - \frac{1}{-R} \right) \] \[ \frac{1}{f} = 0.4 \left( \frac{1}{R} + \frac{1}{R} \right) \] \[ \frac{1}{f} = 0.4 \left( \frac{2}{R} \right) = \frac{0.8}{R} \] Inverting the equation to find \( f \): \[ f = \frac{R}{0.8} \] To find the ratio \( f/R \): \[ \frac{f}{R} = \frac{1}{0.8} = \frac{10}{8} = 1.25 \]
Step 4: Final Answer:
The value of \( f/R \) is 1.25.
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