5.5 Thin Lenses and Mirrors, and Aberrations

Thin lens/mirror equation

The thin lens equation relates object distance (d_o), image distance (d_i), and focal length (f): 1/f = 1/d_o + 1/d_i. This same equation applies to both lenses and curved mirrors. Sign conventions matter: real images/converging elements typically use positive f and d_i, while virtual images use negative values.

Magnification and image properties

Magnification (m) = -d_i/d_o = h_i/h_o. A negative m means the image is inverted; positive means upright. If |m| > 1, the image is enlarged; if |m| < 1, it's reduced. Images can be real (light actually converges, projectable, formed by converging elements when object is outside focal length) or virtual (light appears to diverge from image location, cannot be projected).

Aberrations

Real lenses/mirrors don't focus light perfectly. Spherical aberration occurs because spherical surfaces don't focus all parallel rays to one exact point, blurring images. Chromatic aberration happens because a lens refracts different wavelengths (colors) by different amounts, causing colored fringing since index of refraction depends on wavelength.

Key terms

Thin lens/mirror equation

1/f = 1/d_o + 1/d_i, relating focal length, object distance, and image distance.

Magnification (m)

m = -d_i/d_o = h_i/h_o; negative means inverted, |m|>1 means enlarged.

Real image

Image formed where light rays actually converge; can be projected on a screen.

Chromatic aberration

Blurring/color fringing caused by different wavelengths of light refracting by different amounts.

Spherical aberration

Blurring caused because spherical lens/mirror surfaces don't focus all parallel rays to exactly one point.

Try an AP-style question

Which aberration occurs because a lens bends different colors by different amounts?

1. Diffraction
2. Spherical aberration
3. Chromatic aberration
4. Total internal reflection