I've been self-learning from a physics textbook called Fundamentals of Physics. I'm doing a bit of everything, but there's this optics problem that I just don't understand. Here's the problem (paraphrased).
A swimming pool has a depth of 200 cm. A small light bulb is suspended 250 cm above the surface of the water. The bottom of the pool is a large plane mirror. At what depth below the mirror is the image of the light bulb? (Water has an index of refraction of 1.33.)
Apparently, the answer is 351 cm, but I keep on getting 1.33*(250 cm)+200 cm = 532.5 cm. I assumed a light ray was coming off the light bulb at a small angle theta to the vertical. It would then refract to get an even smaller angle phi in the water. The light ray in the water would then reflect, and you would see the image on the extension of the reflection. However, the image wouldn't be shifted to the left or right, so you would also see the image on a straight axis below the light bulb. I then used the small angle approximations (sinx=tanx=x) and a bit of geometry to get my answer.
Can anyone explain where I went wrong? Or is there a typo in the textbook?