Question

The critical angle for a medium is 60 degree . The refractive index of the medium is

Answer 1

Answer :

✏ Refractive index of medium = $\frac{2}{\sqrt{3}}$

Solution :

➡ Given:

✏ Critical angle of medium = 60$\degree$

➡ To Find:

✏ The refractive index of the medium.

➡ Concept:

✏ Criticle angle is the angle made in denser medium for which the angle of refraction in rarer medium is 90$\degree.$

✏ When angle in denser medium is more then criticle angle the light ray reflects back in denser medium following the laws of reflection and the interface behaves like a perfectly reflecting mirror.

➡ Formula:

✏ Formula of refractive index in terms of criticle angle is given by

$\huge \star \: \underline{ \boxed{ \bold{ \rm{ \pink{ \huge{ \mu = \frac{1}{ \sin{c} }}}}}}} \: \huge \star$

➡ Terms indication:

✏ $\mu$ denotes refractive index of medium.

✏ C denotes criticle angle of medium.

➡ Calculation:

$\mapsto \rm \: \mu = \frac{1}{ \sin60 \degree } \\ \\ \mapsto \rm \: sin60 \degree = \frac{ \sqrt{3} }{2} \\ \\ \mapsto \: \underline{ \boxed{ \bold{ \rm{ \orange{ \mu = \frac{2}{ \sqrt{3}}}}}} } \: \red{ \star}$

➡ Additional information:

• Refractive index is an unitless quantity.
• Refractive index is a dimensionless quantity.

Answer 2

$\large \underline{ \red{ \boxed{ \bf \orange{Required \: Answer}}}}$