Converging lens and its focal length, f

1. Optical axis Converging lens and its focal length, f Light collection: The parallel rays pass through the lens and converge at the focal point. The parallel rays can come from the left or right of the lens. • A thin lens has two focal points, corresponding to parallel rays from the left and from the right. • A thin lens is one in which the distance between the surface of the lens and the center of the lens is negligible compared with the focal length, f.

2. Diverging lens and its focal length, f The parallel rays diverge after passing through the diverging lens. The focal point is the point where the rays appear to have originated. Light collection?

3. Imaging Every point of the object is a point source of light with the rays going in all possible directions. All the rays originating from a point P of the object that go through the lens are also going through another point P’ behind the lens. This is the essence of imaging by the lens. For every point of an object there are three principal rays emanating from it, which are especially convenient to trace.

4. f l • Three principal rays emanating from every point of the object: • Goes parallel to the axis of the lens on the front side and through the focal point on the back side. • Goes through the center of the lens and does not get refracted. • Goes through the focal point on the front side and parallel to the axis of the lens on the back side.

5. Ray Diagram for Converging Lens. The object is further away from the lens than the front focal point, l > f f l • The image is real – the light actually goes through the image location. • The image is inverted. Where do you find this type of image formation?

6. Ray Diagram for Converging Lens. The object is closer to the lens than the front focal point, l < f l f • The image is virtual – the light only appear to come from the image location. The image can only be seen through the lens, not on a screen. • The image is upright and is always magnified. Where do you find this type of image formation?

7. Ray Diagram for Converging Lens. The situation is pretty much the same no matter where the object is located. f l • The image is virtual, and can only be seen through the lens. • The image is upright and is always reduced in size compared with the object. Where do you find this type of image formation?

8. Lens Equation The equation connecting the distances from the object to the lens, l, and from the lens to the image, l’.l’ and l’are both considered positive for the case shown. They become equal, when l = l ’ = 2f

9. Lens magnification The two shaded triangles, blue and gold, are right-angled and similar. Therefore, for the lens magnification, M, we have:The “-” sign is taken to signify the fact that the image is inverted. http://www.mtholyoke.edu/~mpeterso/classes/phys301/geomopti/lenses.html

10. Real, inverted reduced (magnified for l < 2f) Virtual, upright, magnified

11. Virtual, upright, reduced

12. What happens to the image if we put an aperture?If we remove the lens?

13. Who has seen the lens?! I O

14. Who has seen the lens?! I O I O

15. Who has seen the lens?! O I I O

16. Lens aberrations, spherical: Ideally, the surface of a lens should be parabolic…Those are very difficult to make, though! Spherical shape is rather close to a parabola for paraxial rays, which are close to the axis of the lens.The rays, which come at greater angles (further away from the axis) converge in a different, closer point.The image of the point O gets blurry…

17. Lens aberrations, chromatic: Regular glass materials are dispersive: indices of refraction are different for different colors.Rays of different colors are refracted through different angles and converge in different points – the image gets blurry!Remedies – try to use a single color illumination or a composite lens compensating for the dispersion.

18. High end microscope objective collect light from wide angles and compensate for all possible aberrations…