The critical angle for total internal reflection at a water–air interface is given by

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

\theta_c = \arcsin\!\left(\dfrac{1}{n}\right)

, where

n

is the index of refraction of water. At an instant when

n=1.333

and

\dfrac{dn}{dt} = -0.001\,\text{min}^{-1}

, determine

\dfrac{d\theta_c}{dt}

in radians per minute. (a)

-8.5\times10^{-4}

(b)

8.5\times10^{-4}

(c)

3.6\times10^{-4}

(d)

1.13\times10^{-3}