Finding apparent depth real depth and refractive index

[RabbitWho]

Homework Statement

refractive index = 1.33 (water)
real depth = 10m

Homework Equations

refractive index = real depth divided by apparent depth

The Attempt at a Solution

I'm going to call apparent depth X

1.33 = 10/x

So I multiply 10/x by 10 so that i have x and 1.33 x 10 is 13.3... that's right, isn't it? but that makes no sense, because the apparent depth must be less than the actual depth.

I know the real answer is 7.52.. what am I doing wrong?

No idea if the problem is with my maths or my physics.

 

[Doc Al]

So I multiply 10/x by 10 so that i have x and 1.33 x 10 is 13.3... that's right, isn't it?

No, not right. If you multiply $\frac{10}{x}$ by 10 you get $\frac{100}{x}$.

You need to get that x out of the denominator, so multiply both sides by x, not 10. (Or you can cross multiply. Or you can invert both sides. Many ways to play the game!)

 

[RabbitWho]

Thank you! that makes sense. I got the answer right now :)