A biconvex lens has a focal length 2/3 times the radius of curvature of either surface. The refractive index of the lens material is

Question

A biconvex lens has a focal length 2/3 times the radius of curvature of either surface. The refractive index of the lens material is (A) 1.75 (B) 1.33 (C) 1.5 (D) 1.0

Tardigrade Admin · Accepted Answer

Using lens makers formula, (1/f) =(μ-1)((1/R1)-(1/R2)). Here, f =(2/3)R, R1 = +R, R2=-R ∴ (1/(23)R) = (μ-1)((1/R)+(1/R)) =( (μ-1)×2/R) ⇒ μ = 1.75

Q. A biconvex lens has a focal length $2/3$ times the radius of curvature of either surface. The refractive index of the lens material is

$1.75$

$1.33$

$1.5$

$1.0$

Using lens makers formula,
$\frac{1}{f} = (μ - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ .
Here, $f = \frac{2}{3} R$ ,
$R_{1} = + R, R_{2} = - R$
$∴ \frac{1}{( 23 ) R} = (μ - 1) (\frac{1}{R} + \frac{1}{R})$
$= \frac{( μ - 1 ) \times 2}{R}$
$\Rightarrow μ = 1.75$

Q. A biconvex lens has a focal length 2/3 times the radius of curvature of either surface. The refractive index of the lens material is

1.75

1.33

1.5

1.0