Question

The refractive index of a convex lens is μ and the radii of curvature of its surfaces are r₁ and r₂. The focal length f of the lens is expressed as
1. \({f} = (μ -1)^{2} (\frac{1}{r_1} - \frac{1}{r_2})\)
2. \({f} = (μ -1)^{} (\frac{1}{r_1} - \frac{1}{r_2})\)
3. \(f = \frac{r_1r_2}{(μ -1)(r_2 - r_1)} \)
4. \(f = \frac{(r_2 - r_1)}{(μ -1)r_1r_2} \)

Answer 1

Correct Answer - Option 3 : \(f = \frac{r_1r_2}{(μ -1)(r_2 - r_1)} \)

The correct answer is option 3) i.e. \(f = \frac{r_1r_2}{(μ -1)(r_2 - r_1)} \)

CONCEPT:

• A spherical lens is a transparent medium bound by two spherical surfaces. These two surfaces can either be convex, concave, or both.
  • ​When a lens has two surfaces of a different radius of curvature, the focal length of the lens is determined using the Lens maker's formula. 

​It is given by:

\(\frac{1}{f} = (μ -1) (\frac{1}{R_1} - \frac{1}{R_2})\)

Where f is the focal length of the lens, μ is the refractive index of the lens, R1 and R2 are the radii of curvature of two surfaces.

EXPLANATION:

Lens maker's formula, \(\frac{1}{f} = (μ -1) (\frac{1}{R_1} - \frac{1}{R_2})\)

\(\frac{1}{f} = (\mu -1) (\frac{1}{r_1} - \frac{1}{r_2}) = \frac{(μ -1)(r_2 - r_1)}{r_1r_2} \)

⇒ \(f = \frac{r_1r_2}{(μ -1)(r_2 - r_1)} \)