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4. Figure 6 shows a curved surface separating a material with index of refraction n, from a material with index n2. The surface forms an image I of object 0. The center of curvature is point C. n2 h B Figure 6 For the ray that 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 AB, the direction changes according to Snell's law, n, sin 0, = n, sin 02. For paraxial rays, 0, and 02 are small, Snell's law can be rewritten as n, tan 6, = n1 tan 62. The magnification is defined as M = (а) Derive the formula for the magnification of the image. (b) If BC = 8 cm, n̟ = 1.00 , n2 = 1.55 , find the image positions and the magnifications corresponding to object distances, p, of (i) 20.0 cm, (ii) 10.0 cm, and (iii) 6.00 cm.

4. Figure 6 shows a curved surface separating a material with index of refraction n, from a material with index n2. The surface forms an image I of object 0. The center of curvature is point C. n2 h B Figure 6 For the ray that 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 AB, the direction changes according to Snell's law, n, sin 0, = n, sin 02. For paraxial rays, 0, and 02 are small, Snell's law can be rewritten as n, tan 6, = n1 tan 62. The magnification is defined as M = (а) Derive the formula for the magnification of the image. (b) If BC = 8 cm, n̟ = 1.00 , n2 = 1.55 , find the image positions and the magnifications corresponding to object distances, p, of (i) 20.0 cm, (ii) 10.0 cm, and (iii) 6.00 cm.

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4. Figure 6 shows a curved surface separating a material with index of refraction n, from a material with index n2. The surface forms an image I of object 0. The center of curvature is point C. n2 h B Figure 6 For the ray that 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 AB, the direction changes according to Snell’s law, n̟ sin 0, = n, sin 0,. For paraxial rays, 0, and 82 are small, Snell's law can be rewritten as n, tan 6, = n, tan 02. The magnification is defined as M = (a) Derive the formula for the magnification of the image. (b) If BC = 8 cm, n̟ = 1.00 , n2 = 1.55 , find the image positions and the magnifications corresponding to object distances, p, of (i) 20.0 cm, (ii) 10.0 cm, and (iii) 6.00 cm.
Transcribed Image Text:4. Figure 6 shows a curved surface separating a material with index of refraction n, from a material with index n2. The surface forms an image I of object 0. The center of curvature is point C. n2 h B Figure 6 For the ray that 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 AB, the direction changes according to Snell’s law, n̟ sin 0, = n, sin 0,. For paraxial rays, 0, and 82 are small, Snell's law can be rewritten as n, tan 6, = n, tan 02. The magnification is defined as M = (a) Derive the formula for the magnification of the image. (b) If BC = 8 cm, n̟ = 1.00 , n2 = 1.55 , find the image positions and the magnifications corresponding to object distances, p, of (i) 20.0 cm, (ii) 10.0 cm, and (iii) 6.00 cm.
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