# Chapter 25 - Optical Instruments - Questions: 20

Radio waves have a very long wavelength, necessitating a large lens. The wavelength of light is much shorter.

#### Work Step by Step

The Rayleigh criterion, equation 25-7, calculates the resolution limit for a lens/mirror of diameter D when using radiation of wavelength $\lambda$. The objects are resolvable if they are separated by a minimum angle $\theta$, where $\theta = \frac{1.22 \lambda}{D}$. The smaller the angle, the better the resolution. With the very long wavelengths of radio waves, a very large diameter D is required for the telescope to have reasonable resolution. Constructing such a large optical telescope is impractical because making the surface of a lens/mirror free of imperfections (i.e., making it smooth) is difficult when the wavelength of the radiation is so small.

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