Question

One type of hologram consists of bright and dark fringes produced on photographic film by interfering laser beams. If the hologram is illuminated with white light, the image will be 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 the phenomenon of multiple image reproduction in different colors when a hologram is illuminated with white light and determine the colors corresponding to the largest and smallest images. Answer: When a hologram is illuminated with white light, it undergoes diffraction, splitting the white light into its constituent colors. Each color interferes constructively at different heights, resulting in multiple images in different colors. The largest image corresponds to the color with the greatest diffraction angle (red), and the smallest image corresponds to the color with the smallest diffraction angle (blue).

Step-by-step solution

a) Explanation for multiple image reproduction in different colors

By definition, white light consists of a combination of all colors in the visible spectrum. When white light passes through a hologram, it undergoes diffraction, which causes different wavelengths (colors) of light to bend by different amounts. The hologram is made by interfering laser beams, which creates specific patterns of constructive and destructive interference at various points on the film. When the white light shines on the hologram, it interacts with these interference patterns resulting in the splitting of the white light into its constituent colors. Each color will interfere constructively at different heights, leading to the formation of multiple images in different colors.

b) Colors corresponding to the largest and smallest images

The colors for the largest and smallest images depend on the diffraction angle, which is determined by the wavelength of the light. The diffraction angle, \(\theta\), is related to the wavelength, \(\lambda\), through the grating equation: sin(\(\theta\)) = \(\frac{n\lambda}{d}\) Where \(n\) is the order of diffraction, and \(d\) is the distance between adjacent bright or dark fringes in the hologram. The largest image will correspond to the color with the greatest diffraction angle, while the smallest image will correspond to the color with the smallest diffraction angle. Since the wavelength of red light is longer than the wavelength of blue light, red light will have a greater diffraction angle than blue light. Therefore, the largest image will be red, and the smallest image will be blue. The other colors of the spectrum will fall in between these two extremes, forming images of intermediate sizes.