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. \(1.25\)

Hint:

Remember:

• Lens maker formula: \[ \frac{1}{f} = (\mu-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
• For double convex lens: \[ R_1 = +R,\qquad R_2 = -R \]

Answer 1

The Correct Option is D

Concept: For a thin lens, lens maker’s formula is: \[ \frac{1}{f} = (\mu -1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] For a symmetric double convex lens: \[ R_1 = +R, \qquad R_2 = -R \]

Step 1: Substitute the radii into lens maker’s formula. \[ \frac{1}{f} = (\mu -1) \left( \frac{1}{R} - \frac{1}{-R} \right) \] \[ \frac{1}{f} = (\mu -1) \left( \frac{1}{R} + \frac{1}{R} \right) \] \[ \frac{1}{f} = (\mu -1)\frac{2}{R} \]

Step 2: Substitute refractive index value. Given: \[ \mu = 1.4 \] \[ \mu -1 = 0.4 \] Thus: \[ \frac{1}{f} = 0.4 \times \frac{2}{R} \] \[ \frac{1}{f} = \frac{0.8}{R} \] \[ f = \frac{R}{0.8} \] \[ f = 1.25R \]

Step 3: Find the required ratio. \[ \frac{f}{R} = 1.25 \] Therefore, \[ \boxed{1.25} \]