Question

One type of hologram consists of bright and dark fringes produced on photographic film by interfering laser beams. If this is illuminated with white light, the image will appear reproduced multiple times, in different pure colors at different sizes. a) Explain why. b) Which colors correspond to the largest and smallest images, and why?

Short answer

Question: Explain why a hologram illuminated with white light appears reproduced in multiple pure colors and different sizes, and identify the colors that correspond to the largest and smallest images. Answer: A hologram illuminated with white light appears reproduced in multiple pure colors and different sizes due to the principle of interference. When the holographic film is illuminated with white light, the interference patterns correspond to different wavelengths of light for each color. This leads to the reconstruction of separate images for each color with varying sizes based on their wavelengths. In the visible spectrum, red has the longest wavelength, and violet has the shortest wavelength. Therefore, the largest image will be formed by the red color, while the smallest image will be formed by the violet color.

Step-by-step solution

Foundation of Holography

Holography is based on the principle of interference, where two coherent light waves, e.g., from a laser, overlap to produce patterns of light and dark spots on a photographic film. These patterns are formed because of the differences in path length and phase relationships between the two beams.

Illumination with white light

When the holographic film is illuminated with white light (which consists of all visible colors), the interference patterns correspond to different wavelengths of light. Since each color has a unique wavelength, this leads to the reconstruction of separate images for each color.

Color separation

This separation occurs as each wavelength reconstructs its interferogram at a slightly different angle, leading to different image sizes due to the differences in wavelength. This phenomenon causes the reproduction of various pure color images with varying sizes when the hologram is illuminated with white light. #b) Which colors correspond to the largest and smallest images, and why?#

Wavelength and image size

The size of the image formed on the hologram depends on the wavelength of light that interacts with the film. Longer wavelengths will produce larger images, while shorter wavelengths will produce smaller images.

Color and wavelength relationship

In the visible spectrum, red has the longest wavelength, while violet has the shortest wavelength. The other colors fall in between, with their wavelengths decreasing in the following order: red, orange, yellow, green, blue, and violet.

Largest and smallest images

Based on the relationship between color, wavelength, and image size, the largest image will be formed by the red color (longest wavelength), while the smallest image will be formed by the violet color (shortest wavelength). The other colors will produce images with sizes ranging between these two extremes in accordance with their wavelengths.

Key concepts

Interference in Physics

Interference is a fundamental concept in physics that describes the process by which two or more waves overlap to produce a new wave pattern. At points where the waves coincide, they can add together to create a wave of greater amplitude through constructive interference, or they can cancel each other out through destructive interference. This phenomenon is particularly crucial in understanding holography, as it is the precise control of interference that allows for the capturing of three-dimensional images on a two-dimensional surface. Holograms are created by recording the patterns made by interfering light waves from a laser onto photographic film, which can later be reconstructed into an image when illuminated.

White Light Spectrum

The white light spectrum is a continuous range of colors produced when light is dispersed by a prism or diffraction grating. White light is a mixture of all the colors that the human eye can perceive, each color corresponding to a different wavelength of light. This decomposition of light into a spectrum occurs because different wavelengths of light bend by varying amounts when they pass through a medium, a process known as dispersion. When white light is used to illuminate a hologram, these different wavelengths are separated out, and the recorded interference patterns uniquely affect each wavelength, producing images in different pure colors.

Wavelength and Color Relationship

The relationship between wavelength and color is a key aspect of understanding light's behavior. Visible light encompasses wavelengths ranging approximately from 380 nm (nanometers) for violet to 700 nm for red. Each color in the visible spectrum corresponds to a specific range of wavelengths. For instance, blue light has shorter wavelengths around 450–495 nm while red light extends towards the longer end of the spectrum. In the context of holography, this relationship determines how each color will behave when interacting with the interference patterns on the holographic film, leading to various sizes and positions of the reconstructed images.

Visible Light Wavelengths

The wavelengths of visible light determine the perceived color. Visible light wavelengths range from about 380 nm (violet) to approximately 700 nm (red). Within this range, each color has a distinct wavelength that can be associated with it, which is the reason we see a sequence of colors in a spectrum. More than just defining color, these wavelengths also influence how light interacts with materials; for example, differences in wavelength are the reason a hologram reflects multiple colors, each in a slightly different manner.

Constructive and Destructive Interference

Constructive and destructive interference are two opposing outcomes of the phenomenon of interference. Constructive interference occurs when waves meet in phase, their crests and troughs aligned such that they combine to form a wave of higher amplitude. Conversely, destructive interference happens when waves meet out of phase, with the crest of one wave meeting the trough of another, essentially cancelling each other out. In the creation of holograms, both types of interference are instrumental in creating the complex patterns that encode the image information. These patterns are then visible when the hologram is viewed under proper lighting, which makes holography a practical application for both constructive and destructive interference in physics.