Which of the following pair is INCORRECT for some transparent media with respect to air? (may consider the most approximate value)

CONCEPT

The critical angle in optics refers to a specific angle of incidence. Beyond this angle, the total internal reflection of light will occur.

\(n_i\times sinθ_i = n_r\times sinθ_r\)

When θ_r becomes 90^o then the angle of incidence is called the critical angle of incidence. θ_cr

\(n_i\times sinθ_{cr} = n_r \times sin90^o\)

\(\Rightarrow n_i \times sinθ_{cr} = n_r\)

Where n_r = refractive index of the medium, n_i = refractive index of air (Rarer medium) (1)

if the angle of incidence of greater than the critical angle of incidence then the light rays get reflected back this phenomenon is called total internal reflection and the material becomes non-transparent.

CALCULATION:

Case 1) when n_r = 1.33 and θ = 48.75^o

\(n_i \times simθ = 1.33\)

\(θ = sin^{-1}(\frac{1}{1.33})\)

θ_cr = 48.753° 

In this case, water will be a transparent media.

Case 2) when n_r = 1.12,  θ = 29.4^o

Calculation of critical angle for crown glass

\(θ_{cr} = sin^{-1}(\frac{1}{1.12})\)

θ_cr = 63.23^o

θ_cr > 29.4° 

therefore crown glass will be transparent 

Case 3) when n_r = 1.62 and θ = 37.31⁰

Calculation of critical angle for dense flint glass

\(θ_{cr} = sin^{-1}(\frac{1}{1.62})\)

θ_cr = 38.11^o

θ_cr > 37.31^o

therefore dense flint glass will also be transparent.

Case 4) when n_r = 2.42 and θ = 24.41

Calculation of critical angle for diamond

\(θ_{cr} = sin^{-1}(\frac{1}{2.42})\)

θ_cr = 24.40^o

θ_cr < 24.41° 

In this case, the critical angle is less than the incident angle therefore the light rays will reflect back.