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

Cameras LensSingle focus lens Zoom Lens (vary distance between the lenses to change the effective focal length (see example)

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 f 1 =  120 mm and a converging lens with f 2 = 42 mm, spaced 60 mm apart. A 10 cm tall object is 500 mm away from the first lens. (a)What are the location, size, and orientation of the image? p 1 = 500 mm q 2 = 97 mm + 60 mm = 157 mm p1p1 p2p2 q2q2 q1q1

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? p q p1p1 p2p2 q2q2 q1q1

Exposure What do we need for a well exposed picture?

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.

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)

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

f D 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 small f-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

f D 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  is proportional to (intensity) -1 or to D . Example: A camera needs a  1 = 1/100 s exposure time to make an photograph at f /16. What exposure time is needed at f /4?

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.

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. crown glass flint glass

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.

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

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

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.

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. a.Find what focal length contact lens is needed for her to see distant objects clearly. b.Find her new near point (with the contacts on).

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). So q = -17 cm and f = -17 cm The minus sign indicates it is a diverging lens. 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.

Microscope The front objective lens produces a real magnified image I 1, which is then further magnified by the eyepiece.

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

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

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

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' = f obj. 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

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).

Reflecting Telescopes Newtonian telescope Cassegrain telescope