Concept explainers
The difference in positions of two rays crossing the principal axis.
Answer to Problem 55P
The difference in positions of two rays crossing the principal axis is
Explanation of Solution
The following figure gives the ray diagram of the two rays.
Write the expression to find the angle of incidence of the first ray.
Here,
Write the relation between the angle of incidence of the first ray and the second ray.
Write the expression for the focal length of the first ray
Write the expression for the distance crossed by the principal axis from the vertex by the first ray.
Write the expression to find the angle of incidence of the second ray.
Here,
Write the relation between the angle of incidence of the first ray and the second ray.
Write the expression for the focal length of the second ray
Write the expression for the distance crossed by the principal axis from the vertex by the second ray.
Write the expression for the difference in positions of two rays crossing the principal axis .
Conclusion:
Substitute
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Therefore, the difference in positions of two rays crossing the principal axis is
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Chapter 36 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
- Figure 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_forwardHow many times will the incident beam in Figure P34.33 (page 922) be reflected by each of the parallel mirrors? Figure P34.33arrow_forwardTwo rays travelling parallel to the principal axis strike a large plano-convex lens having a refractive index of 1.60 (Fig. P23.54). If the convex face is spherical, a ray near the edge does not pass through the local point (spherical aberration occurs). Assume this face has a radius of curvature of R = 20.0 cm and the two rays are at distances h1 = 0.500 cm and h2 = 12.0 cm from the principal axis. Find the difference x in the position where each crosses the principal axis. Figure P23.54arrow_forward
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