A scuba diver training in a pool looks at his instructor as shown in Figure 25.53. What angle does the ray from the instructor’s face make with the perpendicular to the water at the point where the ray enters? The angle between the ray in the water and the perpendicular to the water is $25.0^{\circ }$.

Video Transcript

This is College Physics Answers with Shaun Dychko. We have this lady standing on the pool deck and the diver is 2.00 meters under the water here; we are told that this ray makes an angle of 25 degrees with respect to the perpendicular to the water surface and we want to know what is this angle between the perpendicular and the line of sight to the lifeguard through the air? So Snell's law says that the first index of refraction multiplied by sin of that angle equals the index of refraction in the second medium times sin of the angle in that second medium and these angles are always measured with respect to perpendicular to the interface between the two media. So our job is to solve for Θ 1 so we can divide both sides by n 1 and get that sin Θ 1 equals n 2sin Θ 2 over n 1 and then take the inverse sin of both sides and so Θ 1 then is the inverse sin of index of refraction of the second medium which is water times sin of Θ 2—the angle between the ray and the perpendicular in that second medium— divided by the index of refraction in the first medium. So this is the inverse sin of 1.33— that's the index of refraction of fresh water which we look up in table [25.1] and that's... for liquids, it's right here—fresh water— and then times sin of 25.0 degrees that we are told divided by 1.00 and that is 34.2 degrees must be this angle between the perpendicular and the line of sight in the air.