Light travels along the length of a 1500 nm-long nanostructure. When a peak of the wave is at one end of the nanostructure, is there a peak or a valley at the other end of the wavelength (a) 500nm and (b) 1000nm?

The total length of the nanostructure is, 1500nm.

The wavelength for case (a) is, 500nm.

The wavelength for case (b) is, 1000nm.

For a longitudinal wave, its wavelength can be defined as the distance between its two consecutive peaks or valleys.

The wavelength of any wave relies upon factors like wave frequency, wave propagation speed, and the propagating medium.

According to the question, the peak of the wave is at one end of the nanostructure, and also the wavelength is the distance between two peaks and valleys of a wave.

Then, the wave showing peak and valley can be drawn as,

Hence, there is a ‘peak’ at the other end of the wave

Similarly, for a wavelength value of 1000nm, the wave having a peak at one end can be drawn as,

Hence, there is a ‘valley’ at the other end of the wave.