# Optics question involving light waves

I tried to solve this question. NO idea if i'm even on the right track.

## Homework Statement

Suppose irradiation of a 100W light bubble (very small - be assumed as point source)
is homogeneous in all directions. Because of low efficiency, only 2% of the electrical
energy will be converted to light energy in the visible range, among which only 10%
passes through the filter. The filter is located at 1m away from the bubble and followed
immediately by a large 1mm-squared photo detector.
Assume that the electrical field of light traveling in the filter is given by:

E(r) = Eo(r)[(∏*10^15) (t - r/(.65c))]

1. Write the mathematical equation of E(r) (ignore the surface loss of the filter).
2. Calculate the frequency of light?
3. Calculate the wavelength of light?
4. What kind of color filter is used?
5. What is the index of refraction of the filter?
6. What is the intensity of light detected (assume quantum efficiency is 0.65)?
7. How many photons will be detected per second?
8. Is the filter likely to have a normal or abnormal dispersion in the filtering wavelength range?

## Homework Equations

$\upsilon$ = frequency
$\lambda$ = wavelength
c= speed of light
$\epsilon$o = vacuum permittivity

## The Attempt at a Solution

1. E(r) = Eo(r)[ωt - r/c]
2. E=hc/$\lambda$
3. $\lambda$$\upsilon$ = c use $\lambda$ from Q2. to solve for $\upsilon$
4. colour depends on the wavelength
5. 0.65/c = n filter / n of medium
make medium air . Therefore n of medium= 1 and nfilter = 0.65
6. I = [(.65cn$\epsilon$o)/2] * E^2
plug in and solve for I
7. NO idea
8. NO idea.