Question

1. A narrow beam of light from a laser travels through air (n = 1.00) and strikes the surface of the water (n = 1.33) in a lake at point A. The angle of incidence is 60 degrees. The depth of the lake is 3.3 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 lakebottom? (b) Considering refraction, how far away from point B would the laser beam strike the lake-bottom?

2. The observer is in air nearly above the object submerged in water (index of refraction 1.33). The depth of the object is 4.5cm. Find the apparent depth of the object. (Hint: Use Snell’s law of refraction and the fact that the angles of incidence and refraction are small, so tan θ ≈ sin θ.)

Answer 1

Problem 1

Part - a

If refraction is not considered then the light ray follows a straight path and hits the bottom surface. Suppose x is the distance where the light ray strikes the bottom surface of the lake, then

by plugging all the values we get

which gives us

Part - b

Using Snell's law we get

by plugging all the values we get

which gives us

again applying

by plugging all the values we get

which gives us