10. The velocity of light in a transparent liquid is 1.8X10cm/second, while in vacuum it is 3X10^3cm/second. Find how much the bottom of the vessel containing this liquid appears to be raised if the depth of the liquid is 25cm.
15.6
To solve this question, we need to apply the concept of refraction since light travels at different speeds in different mediums. The change in velocity of light when it passes from one medium to another is responsible for bending or changing its direction.
The formula that relates the velocity of light in different mediums is known as Snell's Law, which is given by:
n₁ * sin(θ₁) = n₂ * sin(θ₂),
where:
- n₁ and n₂ are the refractive indices of the initial and final media, respectively.
- θ₁ and θ₂ are the angles of incidence and refraction, respectively.
In this scenario, the initial medium is vacuum (which has a refractive index of 1), and the final medium is the transparent liquid. We are given the values for the velocities of light in these mediums, but we need to calculate the refractive index of the liquid.
Let's use Snell's Law to find the refractive index of the liquid:
1 * sin(θ₁) = n₂ * sin(θ₂).
Since the angle of incidence (θ₁) is 0 degrees (light is traveling vertically downward), the sin(θ₁) term becomes 0. Therefore, our equation simplifies to:
0 = n₂ * sin(θ₂).
This implies that sin(θ₂) must also be equal to 0. The only angle that satisfies this condition is 0 degrees (θ₂ = 0). However, since the angle of refraction is zero, the bottom of the vessel containing the liquid will not appear raised.
Hence, the bottom of the vessel containing the transparent liquid will appear to be at the same level as it actually is, despite the change in velocity of light.