Question

A special high-dispersion material has indexes of refraction nviolet = 1.7 for violet light and nred = nviolet - 0.13 for red light. If white light is incident on the top of the block at an angle of 34�� with respect to the normal, by what distance in centimeters would violet and red light be separated by the time they reached the bottom of the glass block, which is 9.6 cm thick?

Answer 1

The separation distance between violet and red light at the bottom of the glass block is approximately 0.71 cm.

Step-by-step explanation:

The separation of violet and red light is due to the dispersion caused by the different indices of refraction for these colors in the high-dispersion material. To calculate this separation distance, we can use the formula:

Separation distance = Thickness of the block × tan(angle of incidence) × (index of refraction for violet - index of refraction for red)

Substituting the given values, where the thickness of the block is 9.6 cm, the angle of incidence is 34 degrees, the index of refraction for violet light is 1.7, and for red light is 1.7 - 0.13, we get:

Separation distance = 9.6 cm × tan(34°) × (1.7 - (1.7 - 0.13))

Solving this expression yields the final answer of approximately 0.71 cm.

Understanding the separation of colors due to dispersion is essential in optics, especially in the design of optical components like prisms and lenses that utilize the phenomenon of refraction at different wavelengths.