A glass plate (n=1.53) that is 0.485 ` mu` m thick and surrounded by air is illuminated by a beam of white light normal to the plate.
(a) What wavelengths (in air) within the limits of the visible spectrum `(lambda = 400 "to" 700 nm)` are intensified in the reflected beam ?
(b) What wavelengths within the visible spectrum are intensified in the transmitted light?

Explanation

To solve the problem, we need to analyze the interference of light waves reflected from the surfaces of a glass plate. The glass plate has a refractive index \( n = 1.53 \) and a thickness of \( t = 0.485 \, \mu m \). We will find the wavelengths of light that are intensified in both the reflected and transmitted beams when illuminated by white light.

### Part (a): Wavelengths Intensified in the Reflected Beam

1. **Determine the Path Difference**:
The path difference \( \Delta x \) for the reflected rays can be calculated using the formula:
\[
\Delta x = 2n t
...