Respuesta :
Answer: A) speed of ligth in water=2.25*10^8 m/s
while the speed of ligth in glass =1.97*10^8 m/s
B) sin(θr)=0.75*sin(θi) ( water)
sin(θr)=0.66*sin(θi) ( glass)
Then sin (θrwater)/(sin (θrglass)=1.14
Explanation: In order to explain this problem we have to consider the expression for speed of light in differents materials, which is given by:
v=c/n where c is the speed of ligth in vacuum and n is the refractive index of the material.
vwater=3*10^8/1.333=2.25*10^8 m/s
vglass=3*10^8/1.53=1.97*10^8 m/s
On the othet hand to calculate the refraction angles in water and glass for the light entering from air we have to take into account the second Snell law which is:
nair*sin (θi)=nwater*sin (θr)
sin (θrwater)= nair/nwater* sin(θi)=0.75*sin (θi)
for the glass
nair*sin (θi)=nglass*sin (θr)
sin (θrglass)= nair/nglass* sin(θi)=0.66*sin (θi)
dividing both we have
sin (θrwater)/(sin (θrglass))=0.75/0.66=1.14
The refraction angle in water is higher than the obtained for the glass.
A) Comparing the speeds of light in water and light in glass, we see that;
The speed of light in water is 1.14 times faster than the speed of light in glass.
B) Comparing Refracted angles in water and glass, we see that;
The refracted angle in water medium is bigger than the refracted angle for glass.
A) The formula to find the speed of light in a medium with a Refractive index of n is given as;
v = c/n
Where;
v is speed of light in that medium
c is speed of light in a vacuum = 3 × 10^(8) m/s
n is Refractive index of medium
We are given that;
Refractive index of glass = 1.52
Refractive index of water = 1.333
Thus;
v_water = (3 × 10^(8))/1.333
v_water = 2.25 × 10^(8) m/s
Similarly;
v_glass = 3 × 10^(8)/1.52
v_glass = 1.974 × 10^(8) m/s
Thus, the speed of light in water is greater than the speed of light in glass.
To know how much greater/faster, we divide;
v_water/v_glass = (2.25 × 10^(8))/(1.974 × 10^(8) m/s) = 1.14
The speed of light in water is 1.14 times faster than the speed of light in glass.
B) To calculate the refraction angles of light in a medium from air, we will use Snell's law to obtain:
n_air × sin (θ_i) = n_medium × sin (θ_r)
Where;
n_air = refraction index of air = 1
θ_i = incident angle
n_medium = refraction index of medium
θ_r = refracted angle
Thus;
For water medium;
sin (θ_r) = (1/1.333) × sin(θ_i)
sin (θ_r) = 0.75sin (θi)
For the glass medium;
sin (θ_r) = (1/1.52) × sin(θi)
sin (θ_r) = 0.66sin (θi)
We can see that refracted angle in water medium is bigger than the refracted angle for glass.
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