A student wants to compare the luminous flux of a light bulb with that of a 1675 lm lamp. The light bulb and the lamp illuminate a sheet of paper equally. The 1675 lm lamp is 1.28 m away from the sheet of paper; the light bulb is 1.08 m away. What is the light bulb's luminous flux?

light bulb: 1675( 1.28/1.08)^2 lm

Thank You; my final answer is 2352.8

To find the light bulb's luminous flux, you can use the inverse square law, which states that the intensity of light decreases as the square of the distance from the source increases.

1. First, find the intensity of light from the 1675 lm lamp at a distance of 1.08 m.
Intensity1 = (Luminous flux1) / (4π * Distance1^2)
where Luminous flux1 = 1675 lm and Distance1 = 1.28 m

Intensity1 = (1675 lm) / (4π * (1.28 m)^2)

2. Next, use the inverse square law to find the luminous flux of the light bulb.
Since the light bulb illuminates the sheet of paper equally, it can be assumed that the intensity of light from both the lamp and the light bulb is the same.

Intensity1 = Intensity2
(Luminous flux1) / (4π * Distance1^2) = (Luminous flux2) / (4π * Distance2^2)
Luminous flux2 = Luminous flux1 * (Distance2^2 / Distance1^2)
where Luminous flux2 is the luminous flux of the light bulb and Distance2 is the distance of the light bulb from the paper.

Luminous flux2 = (1675 lm) * ((1.08 m)^2 / (1.28 m)^2)

3. Calculate the luminous flux of the light bulb.
Luminous flux2 = (1675 lm) * (1.1664 / 1.6384)
Luminous flux2 ≈ 1181.89 lm

Therefore, the light bulb's luminous flux is approximately 1181.89 lm.

To find the light bulb's luminous flux, we need to use the inverse square law of light intensity. The formula is:

I₁ / I₂ = (D₂ / D₁)²

Where I₁ and I₂ are the light intensities, and D₁ and D₂ are the distances from the light source to the illuminated object.

In this case, I₁ is the luminous flux of the 1675 lm lamp, and I₂ is the luminous flux of the light bulb. D₁ is 1.28 m (distance from the 1675 lm lamp to the sheet of paper), and D₂ is 1.08 m (distance from the light bulb to the sheet of paper).

First, we need to calculate the light intensity of the 1675 lm lamp at the distance of 1.08 m using the formula:

I₁ / I₂ = (D₂ / D₁)²
I₂ = I₁ / (D₂ / D₁)²

Substituting the values:
I₂ = 1675 lm / (1.08 m / 1.28 m)²

Simplifying the equation:
I₂ = 1675 lm / (0.84375)²

Calculating the denominator:
0.84375² = 0.7109375

Substituting it back into the equation:
I₂ = 1675 lm / 0.7109375

Finally, calculating the luminous flux of the light bulb:
I₂ ≈ 2359.22 lm

Therefore, the light bulb's luminous flux is approximately 2359.22 lm.