If a hologram is recorded using monochromatic light at one wavelength but its image is viewed at another wavelength, say \(10 \%\) shorter, what will you see? What if it is viewed using light of exactly half the original wavelength?

In the context of holography, monochromatic light plays a pivotal role. Monochromatic light is essentially light of a single wavelength, without any other wavelengths present. It is crucial in creating holograms, which rely on coherent light to record an image. The term 'coherent' means that the light waves are consistent in phase and frequency, a requirement for producing clear holographic images.

When light is monochromatic, it is easier to control and predict the interactions between the light waves and the holographic medium. The recording medium captures the interference pattern, which occurs due to the differences in path lengths traveled by the two sets of light waves: the reference wave and the object wave that has deflected off the object being holographed. Without monochromatic light, these patterns could be more complex, leading to ambiguity in the holographic reconstruction.

Using monochromatic light simplifies the process, allowing for a highly accurate reproduction of the original scene when the hologram is later illuminated with a light source of the same wavelength. Any deviation from the original recording wavelength in viewing can lead to changes in the reconstructed image’s appearance, including color shifts and distortion, as we observe in the exercise provided.

The term phase difference is central to understanding the behavior of waves, including those that make up the light used to create and view holograms. It refers to the offset between two waves at a given point in time and space. Imagine two waves moving through space; if the peaks and troughs line up perfectly, they are said to be 'in phase', but if they are offset, a phase difference exists.

Holography involves recording and reconstructing the phase differences between the reference wave and object wave. These differences are translated into the interference patterns encoded onto the hologram. When viewing a hologram with the same wavelength as the recording light, the reconstructed image properly aligns with these recorded patterns, resulting in a clear, accurate image.

However, when viewing the hologram with light of a different wavelength, the phase difference between the reconstructed waves can alter. This change in phase can cause the image to distort because the interference patterns no longer align as they did during the recording. The degree of distortion depends on the extent of the change in wavelength; smaller changes may yield subtle distortion, while larger changes may lead to significant or even unrecognizable distortions.

The phenomenon of blueshift refers to the increase in frequency (and corresponding decrease in wavelength) of light waves or other electromagnetic waves. This shift toward the blue end of the visible spectrum occurs when the distance between the observer and the source of the waves decreases.

In the case of viewing a hologram with light of a different wavelength than it was recorded with, the term 'blueshift' describes the effect observed when the viewing light’s wavelength is shorter. For instance, as mentioned in the exercise solution, if viewing wavelengths are 10% shorter or exactly half the original recording wavelength, the colors within a hologram appear blueshifted. This is because each color is perceived at a specific wavelength range, and when these wavelengths shorten, the color's appearance shifts to a higher frequency, often resulting in a more blue or violet hue.

This color change is a direct result of the altered phase differences recorded at one wavelength and then reconstructed with another. The blueshift, while it may lend an aesthetically different appeal to the hologram, can also serve as an unintended distortion, potentially making it difficult to recognize the original colors and features of the recorded scene.