Question

On a calm, bright day, you're scuba diving in a deep lake (n = 1.34), 6.00 m away from your sailboat in the horizontal direction. When you are 2.80 m below the surface, the top of the sailboat mast appears to you to be in a direction 32.0° from vertical. Calculate the height of the mast.

Answer 1

320 n=1.34 2.8 m Scuba driver 6 m

from the figure the angle of refraction r = 32° n sin i = n, sin r (1) sin i = (1.34) sin 32° i = sin(0.71) i = 45.240 ZABC = 90-i = 44.750 AABC, tan (44.759) = 48 ... (1) In AABC, CB = HB - DE = 6 - DE tan 32° - DE 2.8 DE =1.75 m CB = 6 - DE = 6-1.75 = 4.2 From equation (1) tan (44.75°) = AB AB = 4.16 m Therefore, the required height of the mass is 4.16 m