Question

When a fish looks up at the surface of a perfectly smooth lake the surface appears dark except inside the circular region directly above it calculate the angle that this illuminate region subtends?

Answer 1

Answer:the lake will not be completely dark

it is due to the phenomenon of TIR(total internal reflection)

the fish will only be able. to see in a circle

rest of the lake would appear dark to it

Explanation:

Answer 2

Answer:

97.2 degrees

Explanation:

It will be the angle for which the angle of refraction for a ray coming out of water would be 90 degrees, because if the ray with any higher angle of incidence would be internally reflected (total internal reflection)

if the angle that the ray makes with vertical  be θc

then

nwater sin(θc)=nair

sin(90 degrees) Or,

sin(θc)= 3/4

θc=48.6 degrees

so

angle subtended by the illuminated region would be 2×48.60=97.2 degrees