Question

Both sides of a convex lens have radius of curvature 40 cm and the refractive index of its glass is 1.5. The focal length of the lens is

• A. 50 cm
• B. 40 cm
• C. 30 cm
• D. -30 cm

Hint:

For a convex lens with equal radii of curvature on both sides, use the lensmaker's formula to find the focal length.

Answer 1

The Correct Option is B

The focal length \( f \) of a lens can be calculated using the lensmaker's formula: \[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] where: \( n \) is the refractive index of the lens material, \( R_1 \) and \( R_2 \) are the radii of curvature of the two surfaces of the lens. For a convex lens, both surfaces have radii of curvature of 40 cm, so: \[ R_1 = 40 \, \text{cm}, \quad R_2 = -40 \, \text{cm} \] Note that \( R_2 \) is negative because the second surface of the lens is curved in the opposite direction. Substitute these values into the lensmaker’s formula: \[ \frac{1}{f} = (1.5 - 1) \left( \frac{1}{40} - \frac{1}{-40} \right) \] \[ \frac{1}{f} = 0.5 \left( \frac{1}{40} + \frac{1}{40} \right) \] \[ \frac{1}{f} = 0.5 \times \frac{2}{40} = \frac{1}{40} \] \[ f = 40 \, \text{cm} \] Thus, the focal length of the lens is 40 cm.