An equilateral prism is a type of optical prism with equal angles. When light passes through the prism, it undergoes refraction at both surfaces, leading to a deviation in its path. The amount of deviation is primarily influenced by the following factors:
Angle of prism: The amount of deviation is dependent on the angle of the prism as it determines the geometry and path length through the material.
Colour of light: Different colors of light (wavelengths) are refracted differently, causing variations in deviation due to dispersion.
Material of the prism: The refractive index of the material affects how much bending occurs, as the deviation is proportional to the refractive index.
However, the size of the prism does not affect the deviation angle. This is because the deviation depends on the material's refractive properties and the geometry of the path within the prism, not on the external dimensions of the prism itself. Therefore, in this context, the size of the prism is irrelevant to the deviation produced.
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The angle of deviation for a prism depends only on the geometry of its cross-section and the optical property of its material, not on how physically large the prism is. We can check this by looking at what each option represents in the deviation formula and ray geometry.
Angle of prism: The prism angle fixes how much the two refracting surfaces are tilted with respect to each other, which directly controls how sharply the ray bends. A larger prism angle produces a larger deviation, so deviation does depend on this.
Colour of light: Different colours of light have different wavelengths, and the refractive index of a transparent material changes slightly with wavelength (dispersion). Since deviation increases with refractive index, different colours bend by different amounts, so deviation does depend on colour.
Material of the prism: Each material has its own refractive index, and a higher refractive index always produces a larger deviation for the same prism angle and angle of incidence. So the choice of material directly changes the deviation.
Size of the prism: If we take two prisms made of the same material, with the same apex angle, but one is twice as large as the other, a ray entering at the same angle of incidence follows a geometrically similar path in both, and exits at the same angle to the original direction. The deviation angle depends only on the shape (apex angle) and the refractive index, not on the physical dimensions of the prism, so scaling the prism up or down does not change the deviation at all.
Comparing all four, the angle, the colour (through dispersion), and the material (through refractive index) each change the deviation, while enlarging or shrinking the prism while keeping its shape and material fixed leaves the deviation unchanged.
Therefore, the correct answer is Size of the prism.
