In a laboratory tank

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

In a laboratory tank, a laser beam in air (refractive index

n_{\text{air}} = 1

) strikes the water surface at a fixed incident angle

\alpha = \dfrac{\pi}{6}

. The refracted angle

\theta

in the water satisfies

\theta = \arcsin\!\left(\dfrac{\sin \alpha}{n_{\text{water}}}\right)

, where the index of refraction of water depends on temperature according to

n_{\text{water}} = 1.33 - 0.0002T

with

T

in degrees Celsius. At the instant when

T = 20^{\circ}\!\text{C}

and

\dfrac{dT}{dt}=0.10^{\circ}\!\text{C/s}

, calculate

\dfrac{d\theta}{dt}

in radians per second.