The refractive index of the material of a double convex lens is 1.5 and its focal length is 5 cm. If the radii of curvature are equal, the value of the radius of curvature (in cm ) is

Question

The refractive index of the material of a double convex lens is 1.5 and its focal length is 5 cm. If the radii of curvature are equal, the value of the radius of curvature (in cm ) is (A) 5.0 (B) 6.5 (C) 8.0 (D) 9.5

Tardigrade Admin · Accepted Answer

(1/f)=(μ-1)((1/R1)-(1/R2)) For double convex lens, R1=R, R2=-R ∴ (1/5)=(1.5-1)((1/R)+(1/R)) or (1/5)=0.5 × (2/R) or R=5 cm

Q. The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 c m$ . If the radii of curvature are equal, the value of the radius of curvature (in $c m$ ) is

5.0

6.5

8.0

9.5

$\frac{1}{f} = (μ - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$
For double convex lens, $R_{1} = R, R_{2} = - R$
$∴ \frac{1}{5} = (1.5 - 1) (\frac{1}{R} + \frac{1}{R})$
or $\frac{1}{5} = 0.5 \times \frac{2}{R}$
or $R = 5 c m$

Q. The refractive index of the material of a double convex lens is 1.5 and its focal length is 5cm. If the radii of curvature are equal, the value of the radius of curvature (in cm ) is

5.0

6.5

8.0

9.5

f1​=(μ−1)(R1​1​−R2​1​) For double convex lens, R1​=R,R2​=−R ∴51​=(1.5−1)(R1​+R1​) or 51​=0.5×R2​ or R=5cm

Q. The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 c m$ . If the radii of curvature are equal, the value of the radius of curvature (in $c m$ ) is

$\frac{1}{f} = (μ - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$
For double convex lens, $R_{1} = R, R_{2} = - R$
$∴ \frac{1}{5} = (1.5 - 1) (\frac{1}{R} + \frac{1}{R})$
or $\frac{1}{5} = 0.5 \times \frac{2}{R}$
or $R = 5 c m$