Question

The critical angle will be maximum when light travels from

• A. glass to air
• B. water to air
• C. glass to water
• D. water to glass

Answer 1

The correct option is C

glass to water

The explanation for the incorrect options:

Option A: Glass to air

When the ray goes from glass (denser) to air (rarer) medium, the critical angle is given by $\sin c=\frac{1}{{\mu }_{ga}}=\frac{1}{{\displaystyle \raisebox{1ex}{${\mu }_g$}\!\left/ \!\raisebox{-1ex}{${\mu }_a$}\right.}}=\frac{1}{{\displaystyle \raisebox{1ex}{$1.5$}\!\left/ \!\raisebox{-1ex}{$1$}\right.}}=\frac{1}{1.5}$

Option B: Water to air

When the ray goes from water (denser) to air (rarer) medium, the critical angle is given by $\sin c=\frac{1}{{\mu }_{wa}}=\frac{1}{{\displaystyle \raisebox{1ex}{${\mu }_w$}\!\left/ \!\raisebox{-1ex}{${\mu }_a$}\right.}}=\frac{1}{{\displaystyle \raisebox{1ex}{$1.33$}\!\left/ \!\raisebox{-1ex}{$1$}\right.}}=\frac{1}{1.33}$

Option D: Water to glass

The critical angle is not observed when the ray goes from water (rarer medium) to glass (denser medium).

Explanation for the correct option:

Option C: Glass to water

1. The critical angle is the angle of incidence for which the angle of refraction is $90°$ when the rays goes from denser to rarer medium.
2. The relationship between the critical angle and the refractive index of denser medium with respect to rarer medium is given by $\sin c=\frac{1}{{\mu }_{21}}$ where $c$ is the critical angle and ${\mu }_{21}$ is the refractive index of denser medium with respect to rarer medium.
3. The refractive index of glass is given by ${\mu }_g=1.5$ and for water is ${\mu }_w=1.33=\frac{4}{3}$.
4. When the ray goes from glass (denser) to water (rarer) medium, the critical angle is given by $\sin c=\frac{1}{{\mu }_{gw}}=\frac{1}{{\displaystyle \raisebox{1ex}{${\mu }_g$}\!\left/ \!\raisebox{-1ex}{${\mu }_w$}\right.}}=\frac{1}{{\displaystyle \raisebox{1ex}{$1.5$}\!\left/ \!\raisebox{-1ex}{$1.33$}\right.}}=\frac{1}{1.127}$
5. The lowest denominator value is $1.127$. So the critical angle would be maximum when the ray goes from glass (denser) to water (rarer) medium.

Thus, the critical angle will be maximum when light travels from glass to water.

Hence, option (C) is correct.