Worksheet: The Dispersive Power of a Prism

In this worksheet, we will practice calculating the dispersive power of a prism, given the refractive indices of the different colours of light passing through it.

Q1:

White light is dispersed by a prism. For the shortest wavelength light in the white light, the prism has a refractive index of 1.48, and for the longest wavelength light, the prism has a refractive index of 1.44. What is the dispersive power of the prism? Give your answer to three decimal places.

Q2:

Which of the following is the term used to refer to the separation of white light into its component wavelengths due to the variation of the refractive index with the wavelength of an object that the white light passes through?

  • ADiffraction
  • BAberration
  • CDeviation
  • DDispersion
  • EDistortion

Q3:

The diagram represents red, green, and blue light being deviated through an angle 𝛼 by a prism. Which of the following correctly describes how πœ†, the wavelength of the light, relates to the angle 𝛼?

  • AAs πœ† increases, 𝛼 increases.
  • BAs πœ† increases, 𝛼 decreases.
  • Cπœ† and 𝛼 are unrelated.

Q4:

A prism has a dispersive power of 0.044. White light is dispersed by the prism. The longest-wavelength light in the white light has a minimum angle of deviation of 25.8∘. What is the minimum angle of deviation of the shortest-wavelength light in the white light? Answer to one decimal place.

Q5:

The dispersive power of a prism is defined as the ratio of the difference between the maximum angles of deviation for the shortest and longest wavelengths of light passing through it to the maximum angle of deviation for the mean wavelength of light passing through it. Which of the following would be the unit of dispersive power?

  • AW/rad
  • Bm/rad
  • CDispersive power is a unitless constant.
  • Drad/m
  • EWβ‹…rad

Q6:

The diagram represents red, green, and blue light being deviated through an angle 𝛼 by a prism. Which of the following correctly describes how πœ†, the wavelength of the light, relates to 𝑛, the refractive index of the prism for a particular wavelength of the light?

  • AAs πœ† increases, 𝑛 increases.
  • BAs πœ† increases, 𝑛 decreases.
  • Cπœ† and 𝑛 are unrelated.

Q7:

White light dispersed by a prism has wavelengths ranging from 400 nm to 700 nm. The 400 nm wavelength light has a minimum angle of deviation of 22.9∘, the 700 nm wavelength light has a minimum angle of deviation of 22.1∘, and the 550 nm wavelength light has a minimum angle of deviation of 22.5∘. What is the dispersive power of the prism? Give your answer to three decimal places.

Q8:

Which of the following formulas correctly relates πœ”ο΅, the dispersive power of a prism, to 𝑛min, the refractive index of the prism for the shortest wavelength of light that passes through it, and 𝑛max, the refractive index of the prism for the longest wavelength of light that passes through it?

  • Aπœ”=𝑛+π‘›βˆ’1minmaxminmax
  • Bπœ”=π‘›βˆ’π‘›βˆ’1minmaxminmax
  • Cπœ”=𝑛+𝑛+1minmaxminmax
  • Dπœ”=π‘›βˆ’π‘›βˆ’1minmaxminmax
  • Eπœ”=π‘›βˆ’π‘›+1minmaxminmax

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