In searching the bottom of a pool at night, a watchman shines a narrow beam of light from his flashlight, h = 1.1 m above the water level, onto the surface of t

Question

this is a physics question I would really appreciate it if someone could help me do it! 

thank you!

 

In searching the bottom of a pool at night, a watchman shines a narrow beam of light from his flashlight, h = 1.1 m above the water level, onto the surface of the water at a point L = 3.3 m from his foot at the edge of the pool. Where does the spot of light hit the bottom of the pool, relative to the edge, if the pool is 2.1 m deep?    

 

 

Answer 1

Hey Arghavan S.,

I know this is an extremely old post, but you know Wyzant asked me to answer it, so here is how I would solve the problem.

Step 1: Calculating the Angle of Incidence (θ1)

First, use the tangent function to find θ1, the angle at which the light hits the water's surface.

Given:

Height of flashlight above water (h): 1.1 meters

Distance from foot to where light hits water (L): 3.3 meters

Calculation:

tan(θ1) = h / L

tan(θ1) = 1.1 / 3.3

θ1 = arctan(1.1 / 3.3)

θ1 ≈ 18.43 degrees (using a calculator)

Step 2: Using Snell's Law to Calculate θ2

Now, use Snell's Law to find θ2, the angle of refraction inside the water.

Snell's Law:

n_air * sin(θ1) = n_water * sin(θ2)

Where:

Refractive index of air (n_air): 1

Refractive index of water (n_water): 1.33

Calculation:

sin(θ2) = n_air / n_water * sin(θ1)

sin(θ2) = 1 / 1.33 * sin(18.43 degrees)

θ2 = arcsin(1 / 1.33 * sin(18.43 degrees))

θ2 ≈ 13.75 degrees (using a calculator)

Step 3: Finding the Distance Inside the Water

Finally, calculate the distance the light travels inside the water to reach the bottom of the pool.

Given:

Depth of the pool: 2.1 meters

Calculation:

tan(θ2) = Depth of pool / Distance from edge to light spot

Distance from edge to light spot = Depth of pool / tan(θ2)

Distance from edge to light spot = 2.1 / tan(13.75 degrees)

Distance from edge to light spot ≈ 8.58 meters (using a calculator)

Therefore, the spot of light will hit the bottom of the pool approximately 8.58 meters from the edge.

Regards,

John

Answer 2

Use

Refractive index = sin i/ Sin r = 1.33 for water

Draw ray diagram showing light bending towards normal when entering from air to water

use Pythagorean triangle properties to relate different distances

I is angle of incidence at water -air interface

r is angle with normal inside water

incase you are not able to get answer, get back to me and I will share video with you

Dr Gulshan Sawhney