Concept explainers
Light is incident on a prism as shown in Figure P38.31. The prism, an equilateral triangle, is made of plastic with an index of refraction of 1.46 for red light and 1.49 for blue light. Assume the apex angle of the prism is 60.00°.
- a. Sketch the approximate paths of the rays for red and blue light as they travel through and then exit the prism.
- b. Determine the measure of dispersion, the angle between the red and blue rays that exit the prism.
Figure P38.31
(a)
The sketch of the appropriate path of the red and blue light rays through the prism.
Answer to Problem 31PQ
The sketch of the appropriate path of the red and blue light rays through the prism is as shown below.
Explanation of Solution
The wavelength of the violet light is
The wavelength of light is inversely proportion to the refractive index of the material through which it is passing.
The wavelength of the violet light is lesser than the wavelength of the red light. Hence, the refractive index of the violet light is more as compared to the refractive index for the red light.
Therefore, violet light refracts more as compared to the red light as shown in the figure below.
Figure-(1)
(b)
The dispersion angle between the red and blue rays when exit the prism.
Answer to Problem 31PQ
The dispersion angle between the red and blue rays when exit the prism is
Explanation of Solution
Write the expression for Snell’s law.
Here, incidence angle is
Further solve the above equation for
The prism diagram on which light is incident at an angle
Figure-(1)
Write the expression for dispersion angle between the red and blue rays when exit the prism.
Here, dispersion angle between the red and blue rays when exit the prism is
Conclusion:
Case (i): For blue light.
Substitute
Solve for
Solve for
Solve for
Substitute
Case (ii): For red light.
Substitute
Solve for
Solve for
Solve for
Substitute
Substitute
Therefore, the dispersion angle between the red and blue rays when exit the prism is
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Chapter 38 Solutions
Student Solutions Manual For Katz's Physics For Scientists And Engineers: Foundations And Connections, Volume 1
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