Conceptual Physics

36.4 - Sample problem: solar radiance

Variables

What is the strategy?

1. Determine the energy of each photon by using Einstein’s equation for the energy of a photon. To determine the photon’s frequency, use
   the relationship between the speed of light, its wavelength and its frequency.


2. Calculate the power of the light entering your eye by using the relationship of intensity, power and surface area.


3. Compare the power of sunlight hitting your eye to the energy of a single photon and calculate how many photons are hitting your eye
   each second.

Physics principles and equations

The energy of a photon is

The relationship between wave speed (in this case, c), wavelength and frequency is

Intensity can be calculated as

Power equals

Take the “typical” wavelength of light

to be 550 nm. What is the energy of a

photon of that light? If you were to

stare into the Sun (a very bad idea!),

how many photons per second would

enter one of your eyes? Use

7.85×10í^7 m^2 for the surface area of

the pupil and assume that the

intensity of sunlight on the Earth’s

surface at your location is 1000 W/m^2.

total energy E

energy of a single photon Ep

frequency of light f

wavelength of light λ = 550×10í (^9) m
Planck’s constant h = 6.63×10í (^34) J·s
intensity of light I = 1000 W/m^2
surface area of one pupil A = 7.85×10í^7 m^2
speed of light c = 3.00×10^8 m/s
number of photons per second N
(^664) Copyright 2007 Kinetic Books Co. Chapter 36