Worksheet: Dispersion

In this worksheet, we will practice calculating the effect of variation of the refractive index of substances on the wavelength of the light that they refract.

Q1:

A narrow beam of light contains light of wavelength 𝜆=580nm and of wavelength 𝜆=550nm. The light passes from polystyrene to air at angle of exactly 30 to the polystyrene-air boundary. The refractive index of the polystyrene for 550 nm wavelength is 1.4930 and the the refractive index of the polystyrene is 1.4920 for 580 nm wavelength light. Use 1.00029 as the refractive index of air for both wavelengths.

What angle separates the directions of propagation of the 580 nm wavelength and the 550 nm wavelength parts of the beam as they enter the air?

The 580 nm wavelength and 550 nm wavelength parts of the emergent light beam are incident on a surface that is perpendicular to the axis of propagation of the emergent beam. At the surface, the 580 nm wavelength and 550 nm wavelength parts of the beam are separated from each other by 1.00 mm. What is the distance between the point of emergence of the beam and this surface?

Q2:

A ray of 6.10×10-m light goes from air into fused quartz at an incident angle of 55.0. Determine at what incident angle 4.70×10-m light must enter flint glass to have the same angle of refraction. Use a value of 1.458 for the refractive index of quartz and use a value of 1.66 for the refractive index of flint glass.

Q3:

A beam of white light goes from air into water with an angle of incidence of 75.0.

At what angle is 6.60×10 m wavelength red light in the beam refracted? Use 1.33 for the refrative index of red light.

At what angle is 4.10×10 m wavelength violet light in the beam refracted? Use 1.34 for the refrative index of violet light.

Q4:

A light ray, ray 1, of wavelength 660 nm and a light ray, ray 2, of wavelength 410 nm are incident on an interface of air and fused quartz. A light ray, ray 3, of wavelength 580 nm and a light ray, ray 4, of wavelength 470 nm are incident on an interface of air and diamond. The difference in speed between ray 1 and ray 2 is compared to that between ray 3 and ray 4. When comparing the pairs of rays, use a value of 1.455 for the refractive index of 660 nm light in fused quartz and a value of 1.468 for the refractive index of 410 nm light in fused quartz. Use a value of 2.417 for the refractive index of 580 nm light in diamond and a value of 2.444 for the refractive index of 470 nm light in diamond. Find the ratio of the difference between the speeds of ray 1 and ray 2 to that between ray 3 and ray 4.

Q5:

Light of wavelength 610 nm is incident on the interior surface of a diamond with a refractive index of 2.415 for that wavelength. Light of wavelength 470 nm is also propagating within the diamond and the refractive index of the diamond for this light is 2.444. The diamond is surrounded by air. What is the difference between the critical angle for the 610 nm wavelength light and the critical angle for the 470 nm wavelength light?

Q6:

A two-colored beam of light consisting of wavelengths of 610 nm and 410 nm propagates through quartz, with the two colors propagating parallel to each other. The beam is incident on a plane interface at an angle of 40 to the interface’s normal, where water is present on the other side of the interface. Find the difference in the angle from the interface’s normal of the two wavelengths when they propagate in water. Use a value of 1.456 for the refractive index of 610 nm wavelength light in quartz and use a value of 1.332 for the refractive index of 610 nm wavelength light in water. Use a value of 1.468 for the refractive index of 410 nm wavelength light in quartz and use a value of 1.342 for the refractive index of 410 nm wavelength light in water.

Q7:

A two-colored beam of light consisting of wavelengths of 660 nm and 470 nm propagates through air, with the two colors propagating parallel to each other. The beam is incident on a rectangular piece of crown glass of thickness 1.33 cm and passes through it to emerge in air. The beam strikes the glass surface at an angle of 33.7 from the normal to the surface. In modeling the propagation of the colors in the beam, use a value of 1.512 for the refractive index of crown glass for the 470 nm wavelength light, and use a value of 1.523 for the refractive index of crown glass for the 660 nm wavelength light.

What is the angle of refraction of 470 nm wavelength light?

What is the angle of refraction of 660 nm wavelength light?

What is the distance between the points where the two colors of light emerge from the glass?

  • A 2 . 0 0 × 1 0 cm
  • B 3 . 6 5 × 1 0 cm
  • C 1 . 1 5 × 1 0 cm
  • D 2 . 6 8 × 1 0 cm
  • E 5 . 9 5 × 1 0 cm

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