Please show your work. 1.) A point source of light is submerged 2.1 m below the

Question

Please show your work.

1.) A point source of light is submerged 2.1 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have?
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2.) A man in a boat is looking straight down at a fish in the water directly beneath him. The fish is looking straight up at the man. They are equidistant from the air-water interface. To the man, the fish appears to be 3.46 m beneath his eyes. To the fish, how far above its eyes does the man appear to be?
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Explanation / Answer

1)

here

refrective index of water = 1.33

refrective index of air = 1

the max radius will be at the critical angle

sin(theta ) = n1 / n2

theta = sin^-1 ( 1 / 1.33)

theta = 48.75 degree

then

tan (theta) = r / 2.1

r = tan(theta) * 2.1

r = tan(48.75) * 2.1

r = 2.39 m

so the maximum radius of the circle will be 2.39 m

2)

You must know that if you look in a medium of index n , the apparent distance is 1/n. For this reason, when you are in a swimming pooland lok at the bottom of the pool, the depth seems smaller
So, if the fish looks from a medium with index n to a medium of index 1, The apparent distance is Dn , so 3.46*1.33 = 4.60m

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