A spherical convex surface of power 5 dioptre separates object and image space of refractive indices 1.0 and (4/3) respectively. The radius of curvature of the surface is

Question

A spherical convex surface of power 5 dioptre separates object and image space of refractive indices 1.0 and (4/3) respectively. The radius of curvature of the surface is (A) 20 cm (B) 1 cm (C) 4 cm (D) 5 cm

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/86011c3c5b13f0e2c533908606041398-.png" /> P=5 D u=∞ then (1/∞)-(4 / 3/f)=(1-4 / 3/R) -(4/3 f)=-(1/3 R) (f/4)=R f=4 R ∴ (100/5)=4 R ⇒ R=(25/5)=5 cm

Q. A spherical convex surface of power $5$ dioptre separates object and image space of refractive indices $1.0$ and $\frac{4}{3}$ respectively. The radius of curvature of the surface is

20 cm

1 cm

4 cm

5 cm

$P = 5 D$
$u = \infty$ then
$\frac{1}{\infty} - \frac{4/3}{f} = \frac{1 - 4/3}{R}$
$- \frac{4}{3 f} = - \frac{1}{3 R}$
$\frac{f}{4} = R$
$f = 4 R$
$∴ \frac{100}{5} = 4 R$
$\Rightarrow R = \frac{25}{5} = 5 c m$

Q. A spherical convex surface of power 5 dioptre separates object and image space of refractive indices 1.0 and 34​ respectively. The radius of curvature of the surface is