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Please show your work. Thank you 1.) A narrow beam of light from a laser travels

ID: 1399472 • Letter: P

Question

Please show your work. Thank you

1.) A narrow beam of light from a laser travels through air

(n = 1.00)

and strikes point A on the surface of the water

(n = 1.33)

in a lake. The angle of incidence is 40°. The depth of the lake is 3.1 m. On the flat lake-bottom is point B, directly below point A.

(a) If refraction did not occur, how far away from point B would the laser beam strike the lake-bottom?
_____________m

(b) Considering refraction, how far away from point B would the laser beam strike the lake-bottom?
_____________m

2.) A stone held just beneath the surface of a swimming pool is released and sinks to the bottom at a constant speed of 0.385 m/s. What is the apparent speed of the stone, as viewed from directly above by an observer who is in air?
_______________m/s

3.) A beam of light is traveling in air and strikes a material. The angles of incidence and refraction are 62.7° and 44.3°, respectively. Obtain the speed of light in the material.
____________m/s

Explanation / Answer

1)

a) Without refraction, the light would hit the bottom at a distance of 3.1 * tan40 = 2.60 m.

b)

by using the snell's law

n1 = 1 (refrective index for air)

n2 =1.33 ( refrective index for water)

1 * sin(40deg) = 1.33 * sin(x)

x = 28.9 degree

then the distance will be

3.1 * tan(28.9 deg) = 1.71 m

the laser beam strike the lake bottom from point B = 1.71 m

2)

Dapp.=Dact.*Na/Nw;
where Dapp. is apparent depth, Dact. is actual depth,
Na is refractive index of air, Nw is refractive index of water.

d(Dapp)/dt=(Dact)/dt*Na/Nw

Dapp = 0.385 * 1 / 1.33

Dapp = 0.289 m/s

the apparent speed of the stone is 0.289 m/s