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

option A

Step-by-step 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 = (radius\ of\ circle)/(verticle\ length)`

`h= (radius)/(tan\theta )`

we know,

`sin \theta = (1)/(n)`

`sin \theta = (1)/(1.33)`

`\theta =sin^(-1)((1)/(1.33))`

from this θ = 48.75°

substitute this in eq ( 1 ) we have

`h= (5)/(tan 48.75)`

h = 4.38

h = 4.4 (approx.)

Hence, the correct answer is option A