White light is incident normally on a glass plate (in air) of thickness \(500 \mathrm{~nm}\) and refractive index of \(1.5 .\) The wavelength (in \(\mathrm{nm}\) ) in the visible region \((400 \mathrm{~nm}-700 \mathrm{~nm})\) that is strongly reflected by the plate is: (1) 450 (2) 600 (3) 400 (4) 500 SECTION - II Reasoning Type This section contains 2 reasoning type questions. Each question has 4 choices (1), \((2),(3)\) and (4), out of which ONLY ONE is correct.

Constructive interference happens when waves combine to make a wave with a larger amplitude. In the context of thin film interference, constructive interference occurs when light waves reflected from the top and bottom surfaces of a film add up to reinforce each other. The key formula is \[2nt = m\lambda\] where: \- \(n\) is the refractive index of the film. \- \(t\) is the film's thickness. \- \(m\) is the order of interference (usually an integer). This condition ensures that the path difference between the two reflected waves is equal to an integer multiple of the wavelength, which is necessary for constructive interference to happen. For a glass plate of 500 nm thickness and refractive index 1.5, this means that the visible wavelength that will show strong reflection is computed using this formula.

Refractive index, denoted as \(n\), is a measure of how much the speed of light is reduced inside a medium compared to the speed in a vacuum. For example, a refractive index of 1.5 means light travels 1.5 times slower in the medium than in a vacuum. This slowing down bends the light, changing its path. When dealing with thin films, the refractive index helps determine the interference pattern. It affects the phase difference between the reflected waves, leading to either constructive or destructive interference. Higher refractive index materials cause more significant bending of light, resulting in more pronounced interference effects.

The visible spectrum is the range of wavelengths of light that can be seen by the human eye, typically between 400 nm and 700 nm. This range includes all the colors of the rainbow, from violet at around 400 nm to red at 700 nm. In the problem given, we focused on finding the wavelength within this visible range that causes strong constructive interference in the thin film. Only wavelengths within this range are visible; anything outside is invisible to the human eye. For our specific problem, solving the formula with the given parameters, we found that a wavelength of 500 nm, which corresponds to green light, is within this visible range and matches one of the provided options.