Thin-lens equation: 1/f = 1/d 0 + 1/d i

Magnification equation: h i /h o = d i /d o

d o and d i are positive for real objects and real images d o and d i are negative for virtual objects and virtual images f is positive for converging lenses f is negative for diverging lenses magnification is positive for an image that is upright, negative for an image that is inverted

Ex. 8 - A 1.70-m tall person is standing 2.50 m in front of a camera. The camera uses a converging lens whose focal length is m. (a) Find the image distance and determine whether the image is real or virtual. (b) Find the magnification and height of the image on the film.

Ex. 9 - An object is placed 7.10 cm to the left of a diverging lens whose focal length is f = cm. (a) Find the image distance and determine whether the image is real or virtual. (b) Obtain the magnification.

When a combination of lenses and/or mirrors is used, the image produced by one lens serves as the object for the next lens.

Ex The objective and eyepiece of a compound microscope are both converging lenses and have focal lengths of f o = 15.0 mm and f e = 25.5 mm. A distance of 61.0 mm separates the lenses. The microscope is being used to examine an object placed d o1 = 24.1 mm in front of the objective. Find the final image distance.

The angular size in radians of an object is approximately equal to the height of the object h o divided by the distance to the object d o, q (in radians) =h o /d o.

Spherical aberration is blurring caused by spherical lenses. Rays far from the principle axis are refracted more than paraxial rays, so they focus closer to the lens than paraxial rays.

Rays are difficult to focus since there is not a unique focal point. The most satisfactory image is formed at the circle of least confusion.

Spherical aberration can be reduced by using a diaphragm to block rays far from the center of the lens. A parabolic surface lens also reduces spherical aberration, but these are expensive.

Chromatic aberration is caused by the fact that the index of refraction varies with wavelength. Shorter waves (violet) are refracted more than longer wavelengths (red). In essence, the lens acts as a prism and disperses the light.

This produces a color fringe around an image. Chromatic aberration can be reduced by using a combination of converging and diverging lenses. This combination is called an “achromatic lens” (without color).