A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is (4/3) and the fish is 12 cm below the water surface, the radius of this circle in cm is

Question

A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is (4/3) and the fish is 12 cm below the water surface, the radius of this circle in cm is (A) 36 √ 7 (B) (36/√ 7) (C) 36 √ 5 (D)  4 √ 5

Tardigrade Admin · Accepted Answer

The situation is shown in figure. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/778f08a04f41dc66f7cb95424fcf696f-.png" /> sinθc =(1/μ) tan θC=(AB/AO) ∴ AB=OA tan θC or AB=(OA/√μ2-1) =(12/√((4)3)2-1)=(36/√ 7)

Q. A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is 12 cm below the water surface, the radius of this circle in cm is

$367$

$\frac{36}{7}$

$365$

$45$

The situation is shown in figure.

$s in θ_{c} = \frac{1}{μ}$
$tan θ_{C} = \frac{A B}{A O}$
$∴ A B = O A tan θ_{C}$
or $A B = \frac{O A}{μ ^{2} - 1}$
$= \frac{12}{( \frac{4}{3} ) ^{2} - 1} = \frac{36}{7}$

Q. A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is 34​ and the fish is 12 cm below the water surface, the radius of this circle in cm is

367​

7​36​

365​

45​