Question

2. Human night vision is very sensitive to blue light but is relatively unaffected by red light. (For this reason, many flashlights intended for use while camping or hiking have a red light setting which won’t affect your ability to see in the darkness of night.) You wish to design a reflective sign which will be visible at night, but not harm the viewer’s night vision. The sign will have a white reflective backing and will be coated by polycarbonate with index of refraction 1.60.

a) For what minimum thickness of polycarbonate will the viewer see no 445 nm light (blue) reflected from the sign?

b) For what minimum thickness of polycarbonate will the viewer see no 445 nm light and the maximum amount of 685 nm (red) light?

Answer 1

a.

For minimum thickness of reflection, $t = \left ( m - \frac{1}{2} \right ) \frac{\lambda}{2n}$

$t = \left ( 0 - \frac{1}{2} \right ) \frac{\lambda}{2n} = \frac{445}{4*1.60} = 69.53 nm\rightarrow Answer$

b.

For minimum thickness of transmission, $t = m \frac{\lambda}{2n}$

$t = \frac{685}{2*1.60} = 214.06 nm \rightarrow Answer$​​​​​​​