Answer:

[tex] \boxed{\sf Angle \: of \: refraction \: (r) = {sin}^{ – 1} ( \frac{1}{2.8} )} [/tex]

Given:

Refractive index of air ( [tex] \sf \mu_{air} [/tex] )= 1

Refractive index of glass slab ( [tex] \sf \mu_{glass} [/tex]) = 1.40

Angle of incidence (i) = 30.0°

To Find:

Angle of refraction (r)

Explanation:

From Snell’s Law:

[tex] \boxed{ \bold{ \sf \mu_{air}sin \ i = \mu_{glass}sin \: r}}[/tex]

[tex] \sf \implies 1 \times sin \: 30 ^ \circ = 1.4sin \:r[/tex]

[tex] \sf sin \:30^ \circ = \frac{1}{2} : [/tex]

[tex] \sf \implies \frac{1}{2} = 1.4 sin \: r[/tex]

[tex] \sf \frac{1}{2} = 1.4 sin \: r \: is \: equivalent \: to \: 1.4 sin \: r = \frac{1}{2} : [/tex]

[tex] \sf \implies 1.4 sin \: r = \frac{1}{2} [/tex]

Dividing both sides by 1.4:

[tex] \sf \implies \frac{\cancel{1.4} sin \: r}{\cancel{1.4}} = \frac{1}{2 \times 1.4} [/tex]

[tex] \sf \implies sin \: r = \frac{1}{2 \times 1.4} [/tex]

[tex] \sf \implies sin \: r = \frac{1}{2.8} [/tex]

[tex] \sf \implies r = {sin}^{ – 1} ( \frac{1}{2.8} )[/tex]

[tex] \therefore[/tex]

[tex] \sf Angle \: of \: refraction \: (r) = {sin}^{ – 1} ( \frac{1}{2.8} )[/tex]

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