$(a)\;\sqrt 2,\frac {1}{\sqrt 2} \\ (b)\;\frac {1}{2}, \sqrt 2 \\ (c)\;\sqrt 3,\frac {2}{\sqrt 3} \\ (d)\;\sqrt 2,\frac {2}{\sqrt 3} $

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Critical angle is angle of incidence at which angle of refraction becomes $90^{\circ}$

Critical angle for material $1= 45^{\circ}$

$\mu =\large\frac{1}{\sin \theta_c}$

$\mu_1 =\large\frac{1}{\sin 45}$

$\qquad= \large\frac{1}{2/\sqrt 2}$

$\mu_1 =\sqrt 2$

Critical angle for material $2= 60^{\circ}$

$\mu_1 =\large\frac{1}{\sin 60}$

$\qquad= \large\frac{1}{\sqrt 3/2}$

$\mu_2= \large\frac{2}{\sqrt 3}$

Hence d is the correct answer.

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