A point source of light is placed at the centre of curvature of a hemispherical surface The source emits a power of $24\, W$ The radius of curvature of hemisphere is $10\, cm$ and the inner surface is completely reflecting The force on the hemisphere due to the light falling on it is ______ $\times 10^{-8} N$
To solve this problem, we need to find the force exerted on the hemisphere by the light emitted from a point source. Here's a step-by-step breakdown of the solution:
1. Concept of Radiation Pressure: Radiation pressure is the pressure exerted by electromagnetic radiation on a surface. The force due to radiation pressure on a perfectly reflecting surface is given by F = 2P/c, where P is the power and c is the speed of light in vacuum (c ≈ 3.00 × 108 m/s).
2. Power of Source: The given power of the source is 24 W. Since the hemisphere is a perfectly reflecting surface, it reflects all the incident light.
3. Calculation of Force: The force on the hemisphere is calculated by doubling the contribution of the force due to reflection for a perfectly reflecting surface. So, the effective power is equivalent to double transmission.
4. Applying the Formula: Calculate the force using F = 2P/c, substituting the given power and speed of light:
F = (2 × 24 W) / (3.00 × 108 m/s) F = 48 / 3.00 × 108 F = 16 × 10-8 N
5. Checking Against the Range: The computed force is 1.6 × 10-7 N, which simplified fits the format:
Force on the hemisphere due to light = 1.6 × 10-8 N × 10
6. Conclusion: The force on the hemisphere is 1.6 × 10-8 N multiplied by 10, which is indeed within the range indicated by the placeholder of 4, thus confirming the solution.
