the ray of son strike the surfaces of a lake at an angle of incidence of 30°.find the angle through which the rays are deviated when they enter water of refrective index 1.33.
Snell's Law says that
sinθ/sin30° = 1/1.33
To find the angle through which the rays are deviated when they enter water, we can use Snell's law. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media involved.
The refractive index of air is approximately 1.00.
Given:
Angle of incidence (i) = 30°
Refractive index of air (n₁) = 1.00
Refractive index of water (n₂) = 1.33
Using Snell's law, we have:
sin(i) / sin(r) = n₂ / n₁
Rearranging the formula, we have:
sin(r) = (n₁ / n₂) * sin(i)
Let's calculate the angle of refraction (r):
sin(r) = (1.00 / 1.33) * sin(30°)
sin(r) = (0.7519) * 0.5
sin(r) = 0.3759
To find the angle, we can take the inverse sine (or arcsine) of both sides:
r = arcsin(0.3759)
r ≈ 0.3845 radians
Converting radians to degrees:
r ≈ 22.05°
Therefore, the angle through which the rays are deviated when they enter water is approximately 22.05°.
To find the angle through which the rays are deviated when they enter water of refractive index 1.33, we can use Snell's Law, which relates the angle of incidence to the angle of refraction.
Snell's Law states:
n1 * sin(θ1) = n2 * sin(θ2)
where:
n1 is the refractive index of the incident medium (in this case, air, which is approximately 1),
θ1 is the angle of incidence,
n2 is the refractive index of the refracting medium (in this case, water, which has a refractive index of 1.33), and
θ2 is the angle of refraction.
Given that the angle of incidence (θ1) is 30° and the refractive index of water (n2) is 1.33, we can rearrange Snell's Law to solve for θ2:
θ2 = arcsin((n1 * sin(θ1)) / n2)
Now let's substitute the values and calculate the angle of refraction:
θ2 = arcsin((1 * sin(30°)) / 1.33)
θ2 = arcsin(0.5 / 1.33)
θ2 ≈ arcsin(0.376)
θ2 ≈ 22°
Therefore, the angle through which the rays are deviated when they enter water of a refractive index of 1.33 is approximately 22°.