In the figure shown, a point object O is placed in air. A spherical boundary of radius of curvature 1.0 m separates various media. A B is the principal axis. The refractive index above A B is 1.6 and below A B is 2.0. The separation (in m) between the images formed due to refraction at spherical surface is

Question

In the figure shown, a point object O is placed in air. A spherical boundary of radius of curvature 1.0 m separates various media. A B is the principal axis. The refractive index above A B is 1.6 and below A B is 2.0. The separation (in m) between the images formed due to refraction at spherical surface is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6b1ebd01fabf8f9fe47bae857850987e-.png" /> I1 ⇒ (1.6/v)-(1/-2)=(1.6-1/+1) ⇒ v1=16 I2 ⇒ (2.0/v)-(1/-2)=(2-1/1) ⇒ v2=4 |v1-v2|=12 m

I1​⇒v1.6​−−21​=+11.6−1​ ⇒v1​=16 I2​⇒v2.0​−−21​=12−1​ ⇒v2​=4 ∣v1​−v2​∣=12m

$I_{1} \Rightarrow \frac{1.6}{v} - \frac{1}{- 2} = \frac{1.6 - 1}{+ 1}$
$\Rightarrow v_{1} = 16$
$I_{2} \Rightarrow \frac{2.0}{v} - \frac{1}{- 2} = \frac{2 - 1}{1}$
$\Rightarrow v_{2} = 4$
$∣ v_{1} - v_{2} ∣ = 12 m$