Question

A ray of light is traveling from glass to air. refractive index of glass is $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$. If the angle of incidence is $50°$, then the deviation of the ray is? Given $\left[\cos ec42°=1.5\right]$

• A. zero degrees
• B. $80$ degrees
• C. $50°-{\sin }^{-1}\left[\frac{\sin 50°}{1.5}\right]$
• D. ${\sin }^{-1}\left[\frac{\sin 50°}{1.5}\right]-50°$

Answer 1

The correct option is B

$80$ degrees

Step 1. Given data:

1. Refractive index of glass $\left({\mu }_{ag}\right)$ = $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=1.5$
2. The angle of incidence $\alpha$ = $50°$,
3. $Criticalangle\left(n\right)=\frac{1}{\sin \theta }$
4. Therefore, $\left[\cos ec42°=\frac{1}{\sin 42°}=1.5\right]$
5. So Critical angle for glass =$42°$

Step 2. Formula used:

We know by linear pair axiom.

$\delta +a+a=180$

Step 3. Calculations:

1. When the angle of incidence in the denser medium is greater than the critical angle, reflection takes place inside the denser medium.
2. So the angle of reflection will be equal to the angle of incidence.
3. Hence, a ray of light incident at an angle of $50°$ in a glass medium undergoes total internal reflection as the angle of incidence $50°$ is greater than the critical angle $42°$.
4. Thus, the Deviation is $\delta =180°-2\alpha$=$180°-2\left(50°\right)=80°$

Hence, the correct option is option B.