Question

A beam of 550 nm light is normally-incident on one thick slab of glass (n = 1.86) (for the purposes of this problem, assume semi-infinite so you’re only worrying about the one interface).

What percentage of the incident power reflects back?

Answer 1

Using the Fresnel equations for normal incidence, the percentage of incident power reflected back by a glass slab with a refractive index of 1.86 when illuminated by 550 nm light is about 9.03%.

Step-by-step explanation:

The question is asking for the percentage of incident power reflected by a thick slab of glass with a known refractive index (n) when 550 nm light hits it. To solve this, we use the Fresnel equations which provide us with the reflectance at the interface between two dielectric (non-conducting) media, such as air and glass. The reflectance (R) for normally incident light is given by the equation:

R = ((n1 - n2)/(n1 + n2))^2

Where n1 is the refractive index of the incident medium (air in this case, with n ≈ 1) and n2 is the refractive index of the glass (n = 1.86 as given). Plugging in the numbers we get:

R = ((1 - 1.86)/(1 + 1.86))^2

Doing the calculations:

R = ((-0.86)/(2.86))^2 ≈ 0.0903 or 9.03%

Thus, the percentage of incident power reflected back by the glass slab is about 9.03%.