Question

Viewed at night from the high diving board at a swimming pool, the light from an underwater bulb forms a bright, 10-ft diameter circle on the surface of the water (n = 1.33). How far below the pool's surface (in feet) is the bulb?
(1) 4.4
(2) 8.8
(3) 3.8
(4) 6.7
(5) 7.5

Answer 1

Answer:

option A

Explanation:

given,

diameter of circle = 10 ft

refractive index of the water = n = 1.33

let the inclined surface of the cone makes an angle θ with vertical line then

$tan \theta = \dfrac{radius\ of\ circle}{verticle\ length}$

$h= \dfrac{radius}{tan\theta }$

we know,

$sin \theta = \dfrac{1}{n}$

$sin \theta = \dfrac{1}{1.33}$

$\theta =sin^{-1}(\dfrac{1}{1.33})$

from this θ = 48.75°

substitute this in eq ( 1 ) we have  

$h= \dfrac{5}{tan 48.75}$

h = 4.38

h = 4.4 (approx.)

Hence, the correct answer is option A