Answer:
Step-by-step explanation:
10% of 100 W = 10 W .
energy of each photon = hν , h is plank's constant and ν is frequency
= hc / λ , c is velocity of light , λ is wavelength
wavelength given λ = 580 x 10⁻⁹ m .
energy of each photon = 6.6 x 10⁻³⁴ x 3 x 10⁸ / 580 x 10⁻⁹
= .034137 x ⁻¹⁷ J
no of photons in 10 W
= 10 / .034137 x ⁻¹⁷
= 292.9 x 10¹⁷
If d be the required distance
no of photons per unit area per second at distance d
= 292.9 x 10¹⁷ / 4πd²
no of photons through the area of eye
= π x (1.65 x 10⁻³)² x 292.9 x 10¹⁷ / 4πd²
= 199.355 x 10¹¹ / d²
199.355 x 10¹¹ / d² = 468 ( given )
d² = 199.355 x 10¹¹ / 468
= .42597 x 10¹¹
= 42597 x 10⁶
d = 206.4 x 10³ m
= 206.3 km.