as light passes from air to water vi/vr=4/3 find the angle of incidence of a ray of light if the angle or refration is 25 degrees 40 minutes (i is the angle of incidence and r is the angle of refraction)
To find the angle of incidence (i), we can use the formula for the refractive index:
n1 * sin(i) = n2 * sin(r)
Given that vi/vr = 4/3, we know that n1/n2 = 4/3.
Since the speed of light in air is higher than the speed of light in water, n1 (refractive index of air) is equal to 1, and n2 (refractive index of water) is equal to 4/3.
Let's solve the equation:
sin(i) = (n2/n1) * sin(r)
sin(i) = (4/3) * sin(25° 40')
First, convert the angle of refraction to decimal degrees:
25° 40' = 25 + 40/60 = 25.667°
Now we can substitute the values into the equation:
sin(i) = (4/3) * sin(25.667°)
To find the angle of incidence, we need to take the inverse sine (sin^-1) of both sides:
i = sin^-1[(4/3) * sin(25.667°)]
Using a scientific calculator, evaluate the expression:
i ≈ 41.176°
Therefore, the approximate angle of incidence (i) is 41.176 degrees.