A Question about Fermat's Principle

In geometrical optics, we know the Fermat's Principle (also named as principle of least optical path length).

Fermat's Principle: The light always chooses the stationary path.

But a question is in the train of it: What is the accurate position when the light refraction occurs?

In a plane rectangular coordinate system, put a point A (0, a) (a>0), a point B (d, -b) (d>0, b>0). And a moving point of motion on the x-axis which named as P(x, 0) (0<x<d). Furthermore, we have a parameter n (n>1). Then when $PA + n \times PB$ reaches the minimum value, what is the value of x?

#Geometry

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$