Respuesta :
Answer:
(a) [tex]n_{2} = \frac{n_{1}sin\theta_{1}}{sin\theta_{2}}[/tex]
(b) [tex]n_{2} = 1.349[/tex]
(c) [tex]v_{1} = 2.04\times 10^{8}\ m/s[/tex]
(d) [tex]v_{2} = 2.22\times 10^{8}\ m/s[/tex]
Solution:
As per the question:
Refractive index of medium 1, [tex]n_{1} = 1.47[/tex]
Angle of refraction for medium 1, [tex]\theta_{1} = 59^{\circ}[/tex]
Angle of refraction for medium 2, [tex]\theta_{1} = 69^{\circ}[/tex]
Now,
(a) The expression for the refractive index of medium 2 is given by using Snell's law:
[tex]n_{1}sin\theta_{1} = n_{2}sin\theta_{2}[/tex]
where
[tex]n_{2}[/tex] = Refractive Index of medium 2
Now,
[tex]n_{2} = \frac{n_{1}sin\theta_{1}}{sin\theta_{2}}[/tex]
(b) The refractive index of medium 2 can be calculated by using the expression in part (a) as:
[tex]n_{2} = \frac{1.47\times sin59^{\circ}}{sin69^{\circ}}[/tex]
[tex]n_{2} = 1.349[/tex]
(c) To calculate the velocity of light in medium 1:
We know that:
[tex]Refractive\ index,\ n = \frac{Speed\ of\ light\ in vacuum,\ c}{Speed\ of\ light\ in\ medium,\ v}[/tex]
Thus for medium 1
[tex]n_{1} = \frac{c}{v_{1}[/tex]
[tex]v_{1} = \frac{c}{n_{1} = \frac{3\times 10^{8}}{1.47} = 2.04\times 10^{8}\ m/s[/tex]
(d) To calculate the velocity of light in medium 2:
For medium 2:
[tex]n_{2} = \frac{c}{v_{2}[/tex]
[tex]v_{2} = \frac{c}{n_{1} = \frac{3\times 10^{8}}{1.349} = 2.22\times 10^{8}\ m/s[/tex]
Answer:
a) [tex]n_{12}=0.918 [/tex]
b) [tex]n_2=1.349[/tex]
c) [tex]v_1=2.041\times 10^{8}\ m.s^{-1}[/tex]
d) [tex]v_2=2.223\times 10^8\ m.s^{-1}[/tex]
Explanation:
Given:
- refractive index of liquid medium 1 (with respect to air), [tex]n_1=1.47[/tex]
- angle of incidence in medium 1, [tex]\theta_1=59^{\circ}[/tex]
- angle of refraction in medium 2, [tex]\theta_2=69^{\circ}[/tex]
(a)
According to Snell's Law:
refractive index of medium 2 with respect to medium 1:
[tex]n_{12}=\frac{sin\ \theta_1}{sin\ \theta_2}[/tex]
[tex]n_{12}=\frac{sin\ 59^{\circ}}{sin\ 69^{\circ}}[/tex]
[tex]n_{12}=0.918 [/tex]
(c)
Now the other form of Snell's law:
[tex]n =\frac{c}{v}[/tex] ..............................(2)
where:
c = speed of light in air
n = refractive index of the medium with respect to air
v = speed of light in medium
Using eq. (2) for medium 1:
[tex]1.47=\frac{3\times 10^{8}}{v_1}[/tex]
[tex]v_1=2.041\times 10^{8}\ m.s^{-1}[/tex]
(d)
Using eq. (2) for medium 2:
[tex]n{12}=\frac{v_1}{v_2}[/tex]
[tex]0.918 =\frac{2.041\times 10^{8}}{v_2}[/tex]
[tex]v_2=2.223\times 10^8\ m.s^{-1}[/tex]
(b)
Now, refractive index of the medium 2 with respect to air
[tex]n_2=\frac{3\times 10^8}{2.223\times 10^8}[/tex]
[tex]n_2=1.349[/tex]
