An opaque cylindrical tank with an open top has a diameter of of 3.00 m and is c

Question

An opaque cylindrical tank with an open top has a diameter of of 3.00 m and is completely filled with water. When the afternoon Sun reaches an angle of 28.0 degree above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. Ho deep is the tank? 8b(Variation). The same tank of the previous problem (diam = 3.00 m; h = 3.39 m) has now no water Find the angle above the horizon below which the afternoon Sun cannot reach the bottom of the tank at all. The lens in the figure at the right is made of glass with n = 1.5. Find its focal length f.

Explanation / Answer

angle of incidence, theta_i = 90 -28

= 62 degrees

let theta_r is the angle of refraction.

Apply, Snell's law

sin(theta_i)/sin(theta_r) = n2/n1

sin(62)/sin(theta_r) = 1.33/1

sin(theta_r) = sin(62)/1.33

sin(theta_r) = 0.6638

theta_r = sin^-1(0.6638)

= 41.6 degrees

let h is the height of cyllinder.

use, tan(theta_r) = d/h

==> h = d/tan(theta_r)

= 3/tan(41.6)

= 3.38 m <<<<<<<------------Answer

use, tan(theta) = h/d

theta = tan^-1(h/d)

= tan^-1(3.39/3)

= 48.5 degrees <<<<<<<------------Answer

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