A ray of light propagates from glass (refractive index = 3/2) to water (refractive index = 4/3). The value of the critical angle is

Question

A ray of light propagates from glass (refractive index = 3/2) to water (refractive index = 4/3). The value of the critical angle is (A)  sin 1( (1/2) )  (B)  sin-1( √(8/9) )  (C)  sin-1( (8/9) )  (D)  sin-1( (5/7) )

Tardigrade Admin · Accepted Answer

Refractive index of glass with respect to water w μg=( a μg/ a μw)=(3 / 2/4 / 3) =(9/8) w μg=(1/ sin C) (9/8)=(1/ sin C) sin C =(8/9) C = sin -1((8/9))

Q. A ray of light propagates from glass (refractive index $= 3/2$ ) to water (refractive index $= 4/3$ ). The value of the critical angle is

$sin^{1} (\frac{1}{2})$

$sin^{- 1} (\frac{8}{9})$

$sin^{- 1} (\frac{8}{9})$

$sin^{- 1} (\frac{5}{7})$

Refractive index of glass with respect to water
$_{w} μ_{g} = \frac{_{a} μ _{g}}{_{a} μ _{w}} = \frac{3/2}{4/3}$
$= \frac{9}{8}_{w} μ_{g} = \frac{1}{s i n C}$
$\frac{9}{8} = \frac{1}{s i n C} sin C = \frac{8}{9} C$
$= sin^{- 1} (\frac{8}{9})$

Q. A ray of light propagates from glass (refractive index =3/2) to water (refractive index =4/3). The value of the critical angle is

sin1(21​)

sin−1(98​​)

sin−1(98​)

sin−1(75​)

Refractive index of glass with respect to water w​μg​=a​μw​a​μg​​=4/33/2​ =89​w​μg​=sinC1​ 89​=sinC1​sinC=98​C =sin−1(98​)

Q. A ray of light propagates from glass (refractive index $= 3/2$ ) to water (refractive index $= 4/3$ ). The value of the critical angle is

$sin^{1} (\frac{1}{2})$

$sin^{- 1} (\frac{8}{9})$

$sin^{- 1} (\frac{8}{9})$

$sin^{- 1} (\frac{5}{7})$

Refractive index of glass with respect to water
$_{w} μ_{g} = \frac{_{a} μ _{g}}{_{a} μ _{w}} = \frac{3/2}{4/3}$
$= \frac{9}{8}_{w} μ_{g} = \frac{1}{s i n C}$
$\frac{9}{8} = \frac{1}{s i n C} sin C = \frac{8}{9} C$
$= sin^{- 1} (\frac{8}{9})$