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Effect of Refraction on Spherical Surface in Light Optics

Explore how light is refracted on a spherical surface, focusing at one point in the focal plane. Solve for deviations and distances in varying media with different refractive indices.

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Effect of Refraction on Spherical Surface in Light Optics

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  1. Waves on a spherical refracting surface

  2. Suppose that light is incident parallel to the optic axis

  3. The ray coming in along the optic axis is not deflected. The ray incident at a height y above the optic axis bends as shown.

  4. With air on the left side and glass on the right we have

  5. This is independent of y, so all incident rays that hit the spherical surface parallel to the optic axis are refracted through F

  6. The refracted ray intersects the optic axis at some point H

  7. Solve for y’ and the distance VG

  8. and we have

  9. and we have

  10. All the light is focused at one point, lying on a plane perpendicular to the optic axis, the so-called focal plane.

  11. Recall that so that From the geometry,

  12. n1 When the external medium has a refractive index n1, the corresponding formula is n2

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