A ray of light traveling inside a transparent medium strikes the boundary with air. If the… — JAMB UTME

A ray of light traveling inside a transparent medium strikes the boundary with air. If the critical angle for total internal reflection at this boundary is $30^\circ$ , what is the refractive index of the medium?

$2.00$ Answer
B
$0.50$
C
$0.87$
D
$1.15$

Answer

The refractive index of the medium is

2.00

For light traveling from a medium into air, the critical angle

C

is related to the refractive index

n

n = \frac{1}{\sin C}

. Substituting

C = 30^\circ

gives

n = \frac{1}{\sin 30^\circ} = \frac{1}{0.5} = 2.00

Step-by-Step Solution

Identify the relationship between critical angle

C

and refractive index

n

The formula for light passing into air is

n = \frac{1}{\sin C}

Total internal reflection occurs when light travels from a denser medium to a less dense medium (air,

n_{air} = 1

) at an angle greater than the critical angle.

Substitute the given critical angle

C = 30^\circ

into the formula

\sin 30^\circ = 0.5

, so

n = \frac{1}{0.5} = 2.00

Taking the reciprocal of

\sin 30^\circ

gives the correct refractive index.

Key Concept

Critical Angle and Refractive Index

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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