A fish looking up through the water sees the outside world, contained in a circular horizon. (4/6) 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. (4/6) 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. sin θC=(1/μ) tan θC=(AB/AO) AB=QA tan θC ∴ 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. $\frac{4}{6}$ 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.
$s in θ_{C} = \frac{1}{μ}$
$t an θ_{C} = \frac{A B}{A O}$
$A B = Q A t an θ_{C}$
$∴ A B = O A t an θ_{C}$
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. 64​ and the fish is 12 cm below the water surface, the radius of this circle in cm is:

367​

7​36​

365​

45​