Concept explainers
The angular dispersion of visible light passing through an equilateral prism.
Answer to Problem 62AP
Explanation of Solution
The ray diagram for the beam through the prism is
Formula to calculate the refraction angle at the first surface of the prism is,
Here,
Substitute
Calculating the value of the angle
Calculating the value of the angle
Calculating the incident angle at the second surface of the prism is,
Formula for the final angle of refraction for the violet light is,
Substitute
Thus, the final refraction angle for violet is
The ray diagram for the beam through the prism is
Formula to calculate the refraction angle at the first surface of the prism is,
Here,
Substitute
Calculating the value of the angle
Calculating the value of the angle
Calculating the incident angle at the second surface of the prism is,
Formula for the final angle of refraction for the red light is,
Substitute
Thus, the final refraction angle for red is
Formula for the angular dispersion is,
Here,
Substitute
Conclusion:
Therefore, the dispersion of the emerging light is
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Chapter 22 Solutions
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- Figure P36.95 shows a thin converging lens for which the radii of curvature of its surfaces have magnitudes of 9.00 cm and 11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8.00 cm. Assume the focal points F1 and F2 of the lens are 5.00 cm from the center of the lens, (a) Determine the index of refraction of the lens material. The lens and mirror are 20.0 cm apart, and an object is placed 8.00 cm to the left of the lens. Determine (b) the position of the filial image and (c) its magnification as seen by the eye in the figure. (d) Is the final image inverted or upright? Explain.arrow_forwardA goldfish is swimming inside a spherical bowl of water having an index of refraction n = 1.333. Suppose the goldfish is p = 10.0 cm from the wall of a howl of radius |R| = 15.0 cm. as in Figure P23.22. Neglecting the refraction of light caused by the wall of the bowl, determine the apparent distance of the goldfish from the wall according to an observer outside the bowl. Figure P23.22arrow_forwardFigure P23.28 shows a curved surface separating a material with index of refraction n1 from a material with index n2. The surface forms an image I of object O. The ray shown in red passes through the surface along a radial line. Its angles of incidence and refraction are both zero, so its direction does not change at the surface. For the ray shown in blue, the direction changes according to n1 sin 1 = n2 sin 2. For paraxial rays, we assume 1 and 2 are small, so we may write n1 tan 1 n2 tan 2. The magnification is defined as M = h/h. Prove that the magnification is given by M = n1q/n2p. Figure P23.28arrow_forward
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