# Thread: minimum time

1. ## minimum time

show that the light waves traveling from P to Q follow the path of minimum time. i know i will be using velocity im jus not sure how, well attached is as far as i have gotten with this problem...i mean would i jus figure out the distance from P to Q and plug that into the formula for velocity, right?IMG.pdf

thanks in advance...

2. Originally Posted by slapmaxwell1
show that the light waves traveling from P to Q follow the path of minimum time. i know i will be using velocity im jus not sure how, well attached is as far as i have gotten with this problem...i mean would i jus figure out the distance from P to Q and plug that into the formula for velocity, right?IMG.pdf

thanks in advance...
t1 = sqrt(d1^2 + x^2)/v1
t2 = sqrt[d2^2 + (a-x)^2]/v2
Total timr t is
t = t1 + t2 = sqrt(d1^2 + x^2)+ sqrt[d2^2 + (a-x)^2]
For least time t
dt/dx = x/v1[sqrt(d1^2 + x^2) - (a-x)/v2sqrt[d2^2 + (a-x)^2] = 0
Tat leads to
sinθ1/v1 = sinθ2/v2, which is the Snell's law.

3. $h1= d_1 cos(\theta_1)$ and $h2= d_2 cos(\theta_2)$ so the total distance from P to Q is $h1+ h2= d_1 cos(\theta_1)+ d_2 cos(\theta_2)$.