Respuesta :
Answer:
(a). The critical angle for the liquid when surrounded by air is 44.37°
(b). The angle of refraction is 26.17°.
Explanation:
Given that,
Incidence angle = 26.7°
Refraction angle = 18.3°
(a). We need to calculate the refraction of liquid
Using Snell's law
[tex]n=\dfrac{\sin i}{\sin r}[/tex]
Put the value into the formula
[tex]n=\dfrac{\sin 26.7}{\sin 18.3}[/tex]
[tex]n=1.43[/tex]
We need to critical angle for the liquid when surrounded by air
Using formula of critical angle
[tex]C=\sin^{-1}(\dfrac{1}{n})[/tex]
Put the value into the formula
[tex]C=\sin^{-1}(\dfrac{1}{1.43})[/tex]
[tex]C=44.37^{\circ}[/tex]
(b). Given that,
Incidence angle = 37.5°
Speed of light in mineral [tex]v=2.17\times10^{8}\ m/s[/tex]
We need to calculate the index of refraction
Using formula of index of refraction
[tex]n=\dfrac{c}{v}[/tex]
Put the value into the formula
[tex]n=\dfrac{3\times10^{8}}{2.17\times10^{8}}[/tex]
[tex]n=1.38[/tex]
We need to calculate the angle of refraction
Using Snell's law
[tex]n=\dfrac{\sin i}{\sin r}[/tex]
[tex]\sin r=\dfrac{\sin i}{n}[/tex]
Put the value into the formula
[tex]\sin r=\dfrac{\sin 37.5}{1.38}[/tex]
[tex]r=\sin^{-1}(\dfrac{\sin 37.5}{1.38})[/tex]
[tex]r=26.17^{\circ}[/tex]
Hence, (a). The critical angle for the liquid when surrounded by air is 44.37°
(b). The angle of refraction is 26.17°.
Answer
a) Angle of incidence i = 26.7°
Angle of refraction r = 18.3°
From Snell’s law index of refraction of the liquid
[tex]n = \dfrac{sin\ i}{sin\ r}[/tex]
[tex]n = \dfrac{sin\ 26.7^0}{sin\ 18.3^0}[/tex]
n = 1.43
So, critical angle
[tex]C= sin^{-1}(\dfrac{1}{n})[/tex]
[tex]C= sin^{-1}(\dfrac{1}{1.43})[/tex]
C = 44.33°
b) Angle of incidence, i = 37.5°
speed of light in mineral oil , v = 2.17 x 10⁸ m/s
speed of light in air, c = 3 x 10⁸ m/s
refractive index of the oil
[tex]n = \dfrac{c}{v}[/tex]
[tex]n = \dfrac{3\times 10^8}{2.17\times 10^8}[/tex]
n = 1.38
again using Snell's law
[tex]n = \dfrac{sin\ i}{sin\ r}[/tex]
[tex]sin\ r = \dfrac{sin\ i}{n}[/tex]
[tex]sin\ r = \dfrac{sin\ 37.5^0}{1.38}[/tex]
[tex] r = sin^{-1}(0.441)[/tex]
r = 26.18°
hence, the angle of refraction is equal to r = 26.18°
