A ray of light travelling from glass to air goes undeviated what should be the angle of incidence

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The correct answer is option 3) i.e. 80°.

CONCEPT:

• Total internal reflection is the phenomena of complete reflection of a ray of light within a medium. This phenomenon occurs when the angle of incidence is greater than a certain limiting angle, called the critical angle (c).

• ​The critical angle of a medium is related to its refractive index by the equation: 

 \(\sin c = \frac{\ 1}{\ \mu}\)​

• The Refractive index is a measure of the bending of a light ray when it passes from one medium into another.

Refractive index (\(\mu\))= \(\frac{\sin i}{\sin r}\)

Where i is the angle of incidence of light and r is the angle of refraction of light.

• Glass is an optically denser medium and the air is an optically rarer medium compared to glass.
• Light bends away from the normal on entering an optically rarer medium. Therefore, r > i.
• Light bends towards the normal on entering an optically denser medium. Therefore, r < i.
• The deviation is the difference between the angle of incidence and angle of refraction.

CALCULATION: 

Given that:

Refractive index (\(\mu\))= 1.5

Angle of incidence (i) = 50º

\(c = \sin ^{-1}\left(\frac{\ 1}{\ 1.5} \right )\)\(= 41.8^\circ\)

\(\therefore\) \(i > c\)

The given light ray, therefore, undergoes total internal reflection as shown:

\(\angle ANO = \angle BNO = 50^\circ\) ( \(\because\) angle of incidence = angle of reflection)

\(\angle ANO = \angle MNP = 50^\circ\) ( \(\because\) vertically opposite angle)

Therefore deviation = difference between incident and reflected angles

Deviation = 180° - (50°  + 50°)  = 80° 

Refractive index (\(\mu\))= 1.5

Angle of incidence (i) = 50º

\(\mu = \frac{\sin 50^{\circ}}{\sin r} \Rightarrow \sin r = \frac{\sin 50^{\circ}}{\mu}\)

\(\sin r = \frac{\sin 50^{\circ}}{1.5}\)

\(r = \sin ^{-1}\left ( \frac{\sin 50^{\circ}}{1.5} \right )\)\(= 30.71^\circ\)

Here the obtained result indicates r < i even though light enters from optically denser to optically rarer medium. This indicates that light has undergone a total internal reflection.

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