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Choose the correct relation for a combination of two prisms to be achromatic. (Where for the first prism: μv = refractive index of the medium in violet light, μr = refractive index of the medium in red light A = angle of the prism; For the second prism: μ′v = refractive index of the medium in violet light, μ′r = refractive index of the medium in red light, A’ = angle of prism.)

Choose the correct relation for a combination of two prisms to be achromatic. (Where for the first prism: μv = refractive index of the medium in violet light, μr = refractive index of the medium in red light A = angle of the prism; For the second prism: μ′v = refractive index of the medium in violet light, μ′r = refractive index of the medium in red light, A’ = angle of prism.) Correct Answer (μ<sub>v</sub> – μ<sub>r</sub>) A = (μ′<sub>v</sub> - μ′<sub>r</sub>) A′

CONCEPT:

  • Dispersion of a Prism: a beam of composite light passes through a prism, it splits into its constituent colours. This phenomenon is called dispersion. The band of colours thus obtained on a screen is called the spectrum.
    •  If white light is used, seven colours are obtained as shown in the figure. The sequence of colours is VIBGYOR, from bottom to top.

 

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  • Deviation without Dispersion (Achromatic Prism): It is possible to combine two prisms of different materials in such a way that each cancels the dispersion due to the other. Thus, the net dispersion is zero but a deviation is produced. The required condition is

(μv – μr) A = (μ′v - μ′r) A′

Where for the first prism: μv = refractive index of the medium in violet light, μr = refractive index of the medium in red light A = angle of the prism; For the second prism: μ′v = refractive index of the medium in violet light, μ′r = refractive index of the medium in red light, A’ = angle of prism.)

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EXPLANATION:

  • The required condition for Achromatic prism is

(μv – μr) A = (μ′v - μ′r) A′

So, Option 1 is correct.

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