Cameras

1. Cameras • Major components • Lens (or combo) • Film (or CCD) • Aperture • Shutter speed

2. Cameras • Lens • Single focus lens • Zoom Lens (vary distance between the lenses to change the effective focal length (see example)

3. p1 q1 q2 p2 p1 = 500 mm q2 = 97 mm + 60 mm = 157 mm Example: A compound camera lens A camera lens is usually a combination of two or more single lenses. Consider a camera lens consisting of a diverging lens with f1 = -120 mm and a converging lens with f2 = 42 mm, spaced 60 mm apart. A 10 cm tall object is 500 mm away from the first lens. • What are the location, size, and orientation of the image?

4. p1 q1 q2 p2 p q Example: A compound camera lens (continued) (b) What is the focal length of the single lens that could produce an image at the location if placed at the midpoint of the lens combination?

5. Exposure • What do we need for a well exposed picture?

6. Exposure • What do we need for a well exposed picture? • Enough Energy on the film (i.e. light) • A more sensitive film needs less light, a less sensitive film needs more light.

7. Film Sensitivity (ISO #) • more sensitive film (e.g. ISO 1000) • Advantage: can take picture in low light • Disadvantage: grainier picture (light sensitive chemicals are larger in size)

8. What factors control how much energy gets to the film? How do I control it? • 1. f-stop • 2. shutter speed Condition • 1a. Opening of lens (Aperture) • 1b. Focal length of lens • 2. Time of exposure

9. D f Camera Lenses: f-stop In camera notation, the “f-stop” means the ratio f/D, where f is the focal length of the lens and D is the diameter of the aperture. f small and D big means smallf-stop (e.g. f/4) a lot of light f big (tele lens) and D small means big f-stop (e.g. f/22) little light

10. D f Camera Lenses: f-stop and exposure times In camera notation, the “f-stop” means the ratio f/D, where f is the focal length of the lens and D is the diameter of the aperture. Thus, f /5.6 means that f/D = 5.6. If f = 50 mm, then D = 8.93 mm. The exposure time t is proportional to (intensity)-1 or to D-2. Example: A camera needs a t1 = 1/100 s exposure time to make an photograph at f/16. What exposure time is needed at f/4?

11. Lens Aberrations Because the index of refraction depends on wavelength, a lens will focus different wavelengths at different focus positions. Cure: Compound lenses made of glasses with different dispersions. Because the focal condition is based on the small angle approximation, spherical lenses focus large-angle rays at different focus positions. Cure: Compound lenses including elements with non-spherical shapes.

12. crown glass flint glass Acromatic Lens By combining a converging lens of crown glass (n = 1.522) with a color-compensating diverging lens of flint glass (n = 1.805), chromatic aberration can be eliminated.

13. Camera and Eye • Camera: change distance between lens and film (focal length f=const) • Eye: distance between lens and retina is constant!!! What can be changed? Focal length f is changed through accomodation.

15. The eye is most sensitive to light of about 550 nm. That is also the wavelength that the Sun emits most strongly at.

16. Far and near point • Far Point (normal eye, relaxed): infinity • Near Point: Minimum distance that can be focused (max. accommodation): 25cm

17. Nearsightedness When fully relaxed, a nearsightedness eye will not be able to focus a distant object on the retina. The image will be in front of the retina. Part a. The far point FP of a nearsighted person is less than infinity. Part b. The correction for nearsightedness involves a diverging lens. Part c.

18. Nearsightedness - Example A nearsighted woman has a near point of 12 cm and a far point of 17 cm (without correction), i.e. she can only focus on objects that are located between these two distances. • Find what focal length contact lens is needed for her to see distant objects clearly. • Find her new near point (with the contacts on).

19. Example: Correcting Nearsightedness A nearsighted woman can see objects clearly only when they are from 12 cm to 17 cm from her naked eye. Find what focal length contact lens is needed for her to see distant objects clearly. Also find her new near point (with the contacts on). We want the contact lens to put the image of a distant object (at infinity) at her far point (17 cm). Soq = -17 cm and The minus sign indicates it is a diverging lens. f = -17 cm To find her new near point, realize that the contacts place the image of the nearest object that can be seen clearly at her naked eye near point (12 cm from her eye). So q = -12 cm and p = 40.8 cm When wearing contacts, she can see clearly from 40.8 cm out to infinity.

20. Microscope The front objective lens produces a real magnified image I1, which is then further magnified by the eyepiece.

21. The Microscope • A specimen to be observed is placed on the stage of a microscope, directly beneath the objective, a converging lens with a relatively short focal length. • The objective creates a magnified real image that is further enlarged by the eyepiece. • The lateral magnification of the objective is • Together, the objective and eyepiece produce a total angular magnification

22. Microscope • Objective lens: converging with small f • Eyepiece: simple magnifier • Objective lens produces real, inverted and enlarged image • Eyepiece enlarges it further and produces a virtual image

23. Microscope • you can’t see the virtual image in the diagram. It is located far away, so that we can view it with a relaxed eye (do2=inf) • Objectiv

25. The Telescope • A simple telescope contains a large-diameter objective lens which collects parallel rays from a distant object and forms a real, inverted image at distance s' = fobj. • The focal length of a telescope objective is very nearly the length of the telescope tube. • The eyepiece functions as a simple magnifier. • The viewer observes an inverted image. • The angular magnification of a telescope is

27. Refracting Telescopes Galilean telescope: Eyepiece is a short-focus diverging lens placed before the focus of the long focal-length objective lens. The resulting magnified image is upright (because the rays don’t cross). Keplerean telescope: Eyepiece is a short-focus converging lens placed after the focus of the long focal-length objective lens. The resulting magnified image is inverted (because the rays cross).

28. Reflecting Telescopes Newtonian telescope Cassegrain telescope