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