Question

A glass convex lens is of refractive index 1.55 with both faces of same radius of curvature. What will be the radius of curvature if focal length is to be 20 cm?

• A. 22 cm
• B. 21 cm
• C. 18 cm
• D. 20 cm

Hint:

For lenses with the same radii of curvature, use the simplified lensmaker’s formula to find the radius when the focal length is known.

Answer 1

The Correct Option is A

Step 1: Using the lensmaker’s formula.
The lensmaker’s formula is given by: \[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] where \( f \) is the focal length, \( n \) is the refractive index, and \( R_1 \) and \( R_2 \) are the radii of curvature of the two faces of the lens. Since both faces have the same radius of curvature, \( R_1 = -R_2 \), the formula simplifies to: \[ \frac{1}{f} = 2(n - 1) \frac{1}{R} \] Step 2: Substituting the given values.
Substitute \( f = 20 \, \text{cm} \) and \( n = 1.55 \) into the equation: \[ \frac{1}{20} = 2(1.55 - 1) \frac{1}{R} \Rightarrow R = 22 \, \text{cm} \] Step 3: Conclusion.
The radius of curvature is \( 22 \, \text{cm} \), which corresponds to option (A).